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LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

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Received     <L/-e~  ,  189  y 

Accession  No.  (Q  7^  ?/        .    Class  No. 


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AN 


INTELLECTUAL   ARITHMETIC, 


UPON  THE 


INDUCTIVE  METHOD, 


INTRODUCTION  TO  WRITTEN  ARITHMETIC. 


BY 

JAMES   S.  EATON,  M.  A., 

INSTRUCTOR    IN    PHILLIPS    ACADEMY,    ANDOVER,    AND    AUTHOR    OF 
"  EASY  LESSONS   IN  MENTAL  ARITHMETIC,"  "  THE  COMMON 

WRITTEN  ARITHMETIC." 


BOSTON: 
TAGGARD     AND     THOMPSON, 

29  CORNHILL. 

SAN  FRANCISCO:  H.  n.  BANCROFT  &  COMPANY. 
1864. 


,/c 


Euteretl,  according  to  Act  of  Congress,  in  the  year  1864,  by 

JAMES    S.  EATON,  M.A., 
In  the  Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


PEEFACE. 


THE  Pestalozzian  or  Inductive  Method  of  teaching  the  science 
of  numbers  is  now  universally  approved  by  intelligent  teachers. 
The  first  attempt  in  this  country  to  apply  this  method  to  Mental 
Arithmetic  resulted  in  the  publication  of  Colburn's  First  Lessons, 
a  work  whose  success  has  not  exceeded  its  merit.  It  was, 
however,  a  useful  experiment  rather  than  a  perfect  realization 
of  the  inductive  system  of  instruction.  That  the  subsequent 
books  of  the  same  class  and  purpose  have  failed  to  correct  its 
defects,  and  thus  meet  the  demand  it  created,  is  due  evidently 
to  their  departure  from  the  true  theory  as  developed  and  exem- 
plified by  Pestalozzi. 

The  Author  of  this  work  has  endeavored  to  improve  upon  all 
his  predecessors,  by  adhering  more  closely  than  even  Colburn 
did  to  the  original  method  of  the  great  Swiss  educator,  and  by 
presenting  at  the  same  time,  in  a  practical  and  attractive  form, 
such  improvements  in  the  application  of  his  principles  as  have 
stood  the  test  of  enlightened  experience. 

In  accordance  with  this  design,  the  subjects  are  so  arranged 
that  each  step  of  the  learner  prepares  him  for  that  which  fol- 
lows. By  this  suggestive  and  natural  order  of  arrangement, 
together  with  copious  illustrations  of  principles  and  applications 
by  means  of  small  concrete  numbers,  the  pupil  is  led  to  a  clear 
apprehension  of  the  properties  and  relations  of  numbers,  and 


4  PREFACE. 

is  enabled  to  understand  everything  as  he  advances,  till  he 
acquires  a  thorough  knowledge  of  the  nature  and  use  of  the 
essential  numerical  operations. 

While  the  general  arrangement  of  the  subjects  and  examples 
is  strictly  progressive  and  logical,  the  difficulty  of  the  problems 
is  occasionally  varied,  in  order  to  prevent  the  weariness  of  a 
long,  unbroken  ascent,  and  to  afford  a  grateful  alternation  of 
effort  and  relaxation,  like  that  experienced  by  the  traveler  in 
crossing  a  country  diversified  by  hill,  valley,  and  plain. 

The  analytical  process  which  this  method  requires  at  every 
step  is  calculated  to  develop  and  strengthen  the  mental  powers, 
and  to  form  the  habit  of  rapid  and  accurate  thought.  Some 
illustrations  of  modes  of  analyzing  questions  have  been  pre- 
sented merely  as  suggestions  to  the  pupil ;  but  the  plan  of  the 
work  does  not  embrace  set  forms  of  analysis  for  the  various 
classes  of  examples,  a  contrivance  little  likely  to  stimulate 
invention  or  promote  self-reliance.  On  the  contrary,  its  dis- 
tinctive feature  is  its  special  adaptation  to  the  mode  of  teaching 
which  leads  the  learner  to  ascertain  for  himself  each  step  to  be 
taken,  to  think  and  reason  independently,  and  to  rely  upon  his 
own  powers  and  resources,  thus  securing  a  vigorous  and  health- 
ful discipline  of  his  intellectual  faculties. 

Though  this  work  is  intended  as  a  connecting  link  between 
the  Primary  and  Written  Arithmetics  of  the  Author,  thus  com- 
pleting the  Series  on  which  he  has  been  so  long  engaged,  it  is 
also  complete  in  itself.  It  presents  a  mental  analysis  of  Arith- 
metic adapted  to  the  younger  pupils  by  its  easy  gradations,  and 
to  advanced  pupils  by  its  scientific  arrangement  and  its  logical 
development  of  the  art  of  computation ;  and  yet  it  has  been 
limited  to  the  true  province  of  Intellectual  Arithmetic,  which  is 
to  serve  as  an  introduction  to  Written  Arithmetic,  and  not  as  a 
substitute  for  it,  as  some  authors  seem  to  imagine. 


PREFACE.  5 

In  the  spirit  of  the  inductive  method,  concrete  numbers  — 
numbers  applied  to  physical  objects  —  have  been  largely  em- 
ployed in  treating  of  each  topic,  as  the  only  fit  preparation  for 
the  exercises  upon  abstract  numbers,  which  are  far  more  difficult 
for  the  youthful  mind  to  grasp. 

A  few  pages  of  Written  Arithmetic  have  been  appended, 
embracing  examples  in  the  ground  rules  and  compound  num- 
bers, which  may  be  profitably  studied  in  connection  with  the 
mental  lessons  illustrating  the  same  principles. 

Fully  aware  of  the  difficulty  of  the  task  he  has  undertaken, 
the  Author  has  spared  no  pains  in  its  execution,  and  he  grate- 
fully acknowledges  his  obligations  for  the  numerous  valuable 
suggestions  with  which  he  has  been  favored  by  several  eminent 
practical  teachers. 

The  favorable  reception  of  the  other  books  of  his  Series,  en- 
courages him  to  hope  that  this  attempt  to  perfect  and  modernize 
the  original  Inductive  System  of  Mental  Arithmetic,  and  adapt  it 
to  the  wants  of  schools  of  the  present  day,  will  meet  with  the 
general  approbation  of  teachers  and  educators. 

PHILLIPS  ACADEMY,  ANDOTBB,  J 
MARCH  14,  1864.  I 


SUGGESTIONS  TO  TEACHERS. 


THE  teacher  who  would  attain  high  success  must  study  meth- 
ods, and  never  take  it  for  granted  that  he  is  perfect  in  his  art. 
Why  does  one  teacher  accomplish  twice  as  much  as  another, 
with  no  greater  expenditure  of  time  and  strength?  Because  he 
has  twice  as  much  skill.  Skill  is  acquired.  It  is  gained  by  ex- 
perimenting; that  is,  by  experience  guided  by  good  judgment, 
and  enlightened  by  the  study  of  methods  and  expedients.  The 
following  Suggestions,  derived  from  long  experience  and  much 
study  of  the  subject  of  teaching  Mental  Arithmetic,  are  sub- 
mitted for  your  consideration,  and  not  as  rules  which  you  are 
to  blindly  follow  without  the  exercise  of  independent  thought. 

1.  Take  great  pains  in  assigning  the  lesson,  adapting  its  length 
to  the  capacity  of  the  class,  stating  explicitly  how  it  is  to  be 
learned  and  in  what  manner  it  is  to  be  recited,  and  giving 
sufficient  time  for  its  thorough  preparation. 

2.  See  that  the  lesson  is  faithfully  studied.    Many  teachers 
waste  time  over  lessons  which  have  not  been  properly  prepared. 
Sometimes  study  a  lesson  with  the  pupils,  to  show  them  how. 

3.  Do  not  require  the  pupils  to  commit  the  questions  to  memory. 
This  is  a  waste  of  time.     Nor  should  they  commit  the  answers, 
t'jctr-ittinri  the  answers  to  that  class  of  examples  which  involve  a 
single  operation  upon  abstract  numbers;  that  is,  such  questions 
as  are  usually  comprised  in  the  tables  of  addition,  subtraction, 
multiplication,  and  division. 

4.  Never  require  a  pupil  to  analyze  questions  according  to  a 
set  form  of  analysis,  but  encourage  originality  in  methods  of 
solution.    The  fewer  words  in  the  solution  the  better,  if  it  is 
correct  and  intelligible.    By  all  means  avoid  long  and  compli- 
cated formulas. 

5.  Do  not  demand  reasons   for  answers  which  require  no 
process  of  analysis.     If  the  child  knows  that  4  from  6  leaves  2, 
what  is  gained  by  requiring  him  to  say.  Because  4  and  2  are  6? 
The  thing  is  no  better  understood,  and  time  is  consumed. 

6.  The  teacher  will  read  the  questions  himself,  the  class  dis- 
pensing with  the  book,  or  he  will   allow  the  pupils  to  have 
the  book  and  read  the  examples,  as  he  may  prefer.     In  ques- 
tions requiring  analysis  the  pupils  should  not  be  called  in  turn, 
but  promiscuously  or  by  cards,  and,  if  the  example  is  read  by  the 
teacher,  time  should  be  given,  after  the  reading,  for  the  class  to 
think,  before  any  pupil  is  designated  to  answer.    Examples  like 
those  in  Lesson  II,  page  11,  may  be  recited  by  the  members  of 
the  class  in  rotation,  the  questions  being  read  rapidly. 

7.  The  answer  to  a  question  requiring  a  process  of  solution 
should  not  be  given  before  the  solution,  but  it  should  be  given 
at  the  conclusion  cf  the  solution.   Nor  should  pupils  be  required, 
as  a  practice,  to  give  what  may  be  called  an  abstract  or  general 
answer  before  the  solution,  like  the  following :  J  of  36  is  -f  of 


SUGGESTIONS  TO  TEACHERS.  7 

how  many  times  -f  of  42?  As  many  times  f  of  42  as  y  of  42  is 
contained  times  in  the  number  of  which  -J-  of  j  of  36  is  J.  Such 
exercises  may  be  good  discipline,  but  there  is  no  need  of  con- 
suming time  on  exercises  merely  for  discipline,  as  the  oppor- 
tunities for  it  in  acquiring  useful  knowledge  are  abundant. 

8.  When  practicable,  it  is  best  that  the  whole  class  should 
stand  at  recitation.    At  any  rate,  the  pupil  who  recites  should 
stand,  and,  if  the  teacher  reads  the  example,  the  pupil  should 
repeat  it  after  him,  before  giving  the  explanation. 

9.  Never  proceed  with  the  recitation  unless  every  member  of 
the  class  is  giving  attention,  but  do  not  try  to  keep  the  atten- 
tion too  long.    Many  expedients  must  be  employed  to  keep  the 
attention  awake.    Sometimes  the  pupils  may  "take  places/' 
sometimes  they  may  be  permitted  to  correct  each  other,  and 
sometimes  a  pupil  may  be  called  at  random  to  finish  a  solution 
commenced  by  another. 

10.  Aim  at  thoroughness  in  every  step.  This  is  much  promoted 
by  frequent  and  judicious  reviews.   With  every  lesson  in  advance 
the  preceding  should  be  reviewed;  and  there  should  be  monthly 
and  quarterly  reviews  beside. 

11.  If  you  suspect  that  a  solution  has  been  committed  to 
memory  without  being    understood,  give  a  similar   original 
question  with  different  numbers. 

12.  Where  it  is  practicable,  illustrate  problems  and  principles 
by  sensible  objects.    Let  fractions  be  illustrated  by  dividing  an 
apple,  a  line,  a  square,  or  some  other  object.  The  tables  of  weights 
and   measures   should   be  taught  according  to  the  method  of 
obiect-teaching,  and  not  abstractly  committed  to  memory. 

13.  As  an  occasional  exercise,  let  each  pupil,  from  memory, 
propose  to  the  pupil  next  above  him  some  question  embraced 
in  the  part  of  the  book  which  has  been  studied,  the  pupil  failing 
to  solve  the  question  put  to  him  losing  his  place;  or,  where 
"place  taking"  is  not  practiced,  let  there  be  a  forfeiture  of 
merits  for  failure,  or  a  gain  for  success. 

14.  Original  questions  similar  to  examples  32  and  33,  page  28, 
to  be  answered  simultaneously  by  the  class,  should  be  proposed 
frequently  and  enunciated  rapidly. 

15.  The  learner  should  seldom  if  ever  be  told  directly  how  to 
perform  any  operation  in  Arithmetic.    Much  less  should  he  have 
the  operation  performed  for  him.    Instead  of  telling  the  pupil 
directly  how  to  go  on,  examine  him,  and  endeavor  to  discover 
in  what  his  difficulty  consists,  and  then,  if  possible,  remove  it. 

16.  The  recitation  should  be  conducted  briskly,  and  it  should 
be  so  managed,  if  practicable,  that  each  pupil  shall  endeavor  to 
solve  every  question  proposed ;  but  it  is  not  necessary  that  the 
whole  lesson  should  be  actually  recited  by  each  pupil. 

17.  But  the  most  important  requisite  to  success  is  to  create  and 
to  sustain  an  interest  in  the  study.    How  can  this  be  done  ?    In 
the  first  place  you  must  be  really  very  much  interested  yourself. 
In  the  second  place,  you  must  teach  well.   And  if  you  are  deeply 
interested  in  the  subject,  you  will  be  very  likely  to  find  out  how 
to  teach  it  skillfully. 


CONTENTS. 


I. 

SECTION!,  pp.  9-25,  contains  addition,  subtraction,  multiplication, 
and  division,  and  numbers  are  expressed  only  by  words.  The  very 
young  pupil  will  be  aided  in  solving  the  examples  by  sensible  objects, 
such  as  knives,  cents,  marbles,  apples,  fingers,  etc. 

II. 

SECTION  II,  pp  26-47,  introduces  the  Arabic  figures  and  Arith- 
metical signs.  The  examples  are  similar  to  those  in  Section  I,  and 
a  little  more  difficult. 

III. 

SECTION  III,  pp.  48-75,  presents  the  elements  of  fractions,  and  op- 
erations upon  whole  numbers  are  continued  and  extended. 

IV. 

SECTION  IV,  pp.  75-92,  defines  fractions,  the  fractional  form  isin- 
troduced,  and  the  principles  of  fractions  are  still  further  developed. 

V. 

SECTION  V,  pp.  93-101,  gives  the  tables  of  compound  numbers  and 
practical  examples  on  the  same 

VI. 

SECTION  VI,  pp.  101-124,  gives  a  variety  of  practical  examples, 
together  with  the  more  complicated  combinations  of  fractions. 

VII. 

SECTION  VII,  pp.  125-138,  introduces  several  notes,  giving  more  or 
less  minute  suggestions  with  reference  to  the  various  operations  in 
fractions. 

VIII. 

SECTION  VHI,  pp.  139-148,  develops  some  of  the  more  important 
principles  in  per  centage. 

IX. 

SECTION  IX,  pp,  149-163,  consists  of  a  few  Lessons  composed  of 
miscellaneous  examples,  together  with  Multiplication  and  Review 

Tables. 

x. 

In  pp.  164-176,  a  few  of  the  more  simple  principles  of  Written 
Arithmetic  are  given.  These  pages  may  be  studied  with  or  after  the 
preceding  pages. 


INTELLECTUAL  ARITHMETIC. 


SECTION  FIRST. 
LESSON  I. 

1.  HENRY  had  one  knife,  and  he  has  found  another; 
how  many  knives  has  he  now  ? 

2.  Charles  bought  an  orange  for  two  cents,  and  an 
apple  for  one  cent  ;   how  many  cents  did  he  pay  for 
both? 

3.  Mary  gave  two  peaches  to  Sarah,  and  kept  two 
herself ;  how  many  peaches  had  she  at  first  ? 

4.  If  you  have  four  marbles  in  one  hand,  and  three 
in  the  other,  how  many  have  you  in  both  ? 

5.  If  you  have  four  fingers  on  each  hand,  how  many 
fingers  have  you  on  both  hands  ? 

6.  James  found  five  apples  under  one  tree,  and  four 
under  another ;  how  many  apples  did  he  find  under 
both  trees  ? 

7.  Addie  has   five  canaries,  and   Ella   has  three  ; 
how  many  canaries  have  they  together  ? 

8.  Robert  had  three  peaches,  but  he  has  given  one 
of  them  away ;  how  many  peaches  has  he  now  ? 

9.  John  having  four  cents,  spent  two  of  them  for 
an  orange  ;  how  many  cents  has  he  now  ? 

10.  David  has  five  cents  in  one  hand,  and  two  cents 
in  the  other  ;  how  many  cents  has  he  in  both  hands  ? 
How  many  more  in  one  hand  than  in  the  other  ? 

11.  Frank  has  six  gray  squirrels,  and  Herbert  has 
three  ;  how  many  squirrels  have  they  both  ? 


10  INTELLECTUAL  [SEC.  I. 

12.  Edwin  has  six  figs,  and  Philip  has  four;  how 
many  more  figs  has  Edwin  than  Philip  ?     How  many 
have  they  both  ? 

13.  William  having  eight  plums,  gave  five  of  them 
to  Louisa ;  how  many  did  he  keep  ?     How  many  less 
did  he  keep  than  he  gave  away  ? 

14.  Edward  has  six  doves,  and  Charles  has  eight ; 
how  many  more   has  Charles  than  Edward  ?     How 
many  have  they  both  ? 

15.  Lewis  bought  a,  pig  for  eight  dollars,  and  sold 
it  for  ten  dollars  ;  how  much  did  he  gain  ? 

16.  A  man  bought  a  sled  for  ten  dollars,  and  sold 
it  for  seven  ;  how  much  did  he  lose  ? 

17.  A  man   owing  ten  dollars,  paid  four  dollars  ; 
how  much  did  he  still  owe  ? 

18.  A  man  owing  ten  dollars,  paid  all  but  four  dol- 
lars ;  how  much  did  he  pay  ? 

19.  Mr.  Adams  sold  a  pig   for  three  dollars,  and 
a  sheep  for  six  dollars ;  how  many  dollars  did  he  re- 
ceive for  both  ? 

20.  Albert  has  eight  rabbits,  and  Arthur  has  two  ; 
how  many  rabbits  have  they  both  ? 

21.  George  found  seven  eggs  in  one  nest,  and  three 
in  another ;  how  many  eggs  did  he  find  f 

22.  Frank  gave  three  cents  for  an  orange,  and  had 
seven  cents  left ;  how  many  cents  had  he  at  first? 

23.  If  a  melon  is  worth  ten  cents,  and  an  orange  is 
worth  four  cents,  how  many  cents  are  they  both  worth  ? 
Ilo\v  much  more  is  the  melon  worth  than  the  orange  ? 

24.  Mary  had  nine  cents,  and  her  mother  gave  her 
three  ;  how  many  cents  had  Mary  then  ? 

25.  Robert  had  ten  peaches,  but  he  has  given  four 
of  them  to  David  ;    how  many  peaches   has  Robert 
now  ?     How  many  more  than  David  ? 

26.  Mr.  Day  bought  a  barrel  of  flour  for  ten  dollars, 
and  sold  it  for  two  dollars  more  than  he  gave  for  it ; 
how  much  did  he  receive  for  it  ? 


ARITHMETIC.  11 

27.  A  boy  having  twelve  walnuts,  gave  away  five 
of  them  ;  how  many  had  he  left  ? 

28.  Bought  a  ton  of  coal  for  ten  dollars,  and  a  cord 
of  wood  for  six  dollars ;    what  did  I  pay  for  both  ? 
How  much  more  for  the  coal  than  for  the  wood  ? 

LESSON  II. 

1.  Two  and  one  are  how  many? 

2.  Three  and  one  are  how  many  ? 

3.  Four  and  one  are  how  many  ? 

4.  Five  and  one  are  how  many  ? 

5.  Six  and  one  are  how   many  ? 

6.  Seven  and  one  are  how  many  ? 

7.  Eight  and  one  are  how  many  ? 

8.  Nine  and  one  are  how  many? 

9.  Ten  and  one  are  how  many? 

10.  Two  and  two  are  how  many  ? 

11.  Three  and  two  are  how  many? 

12.  Four  and  two  are  how  many? 

13.  Five  and  two  are   how  many  ? 

14.  Six  and  two  are  how  many? 

15.  Seven  and  two  are  how  many? 

1 6.  Eight  and  two  are  how  many  ? 

17.  Nine  and  two  are  how  many  ? 

18.  Ten  and  two  are  how  many? 

19.  Two  and  three   are  how  many? 

20.  Three  and  three  are  how  many? 

21.  Four  and  three  are  how  many? 

22.  Five  and  three  are  how  many  ? 

23.  Six  and  three  are  how  many  ? 

24.  Seven  and  three  are  how  many  ? 

25.  Eight  and  three  are  how  many  ? 

26.  Nine  and  three  are  how  many? 

27.  Ten  and  three  are  how  many? 

28.  Two  and  four  are  how  many  ? 

29.  Three  and  four  are  how   many  ? 


2  INTELLECTUAL  [SEC.  I. 

30.  Four  and  four  are  how  many? 

3 1 .  Five  and  four  are  how  many  ? 

32.  Six  and  four  are  how  many  ? 

33.  Seven  and  four  are   how  many? 

34.  Eight  and  four  are  how  many? 

35.  Nine  and  four  are   how  many  ? 

36.  Ten  and  four  are   how  many  ? 

37.  Two  and  five   are   how  many? 

38.  Three  and  five  are  how  many  ? 

39.  Four  and  five  are  how  many  ? 

40.  Five  and   five   are  how  many  ? 

41.  Six  and  five  are  how   many  ? 

42.  Seven  and  five  are    how  many? 

43.  Eight  and  five   are  how  many  ? 

44.  Nine  and  five   are   how  many? 

45.  Ten  and  five  are  how  many  ? 

46.  Two  and  six  are  how  many? 

47.  Three   and   six  are  how  many? 

48.  Four  and    six  are  how  many? 

49.  Five   and  six  are  how  many  ? 

50.  Six  and  six   are  how   many? 

51.  Seven  and  six  are  how  many  ? 

52.  Eight  and  six  are  how  many? 

53.  Nine  and  six  are  how  many? 

54.  Ten  and  six  are   how  many? 

55.  Two  and  seven  are   how  many  ? 

56.  Three  and   seven  are  how  many? 

57.  Four  and  seven  are   how  many  ? 

58.  Five  and  seven  are  how  many? 

59.  Six  and   seven  are   how  many  ? 

60.  Seven  and  seven  are  how  many  ? 

61.  Eight   and  seven  are   how  many? 

62.  Nine  and  seven  are  how  many  ? 

63.  Ten  and  seven   are  how  many  ? 

64.  Two  and   eight  are   how  many? 

65.  Three  and  eight  are  how  many  ? 

66.  Four  and  eight  are  how  many? 


I.ES.  III.]  ARITHMETIC.  13 

67.  Five  and  eight  are  how  many? 

68.  Six  and   eight  are  how  many? 

69.  Seven  and  eight  are  how  many? 

70.  Eight  and  eight  are  how  many? 

71.  Nine  and  eight  are  how  many? 

72.  Ten  and  eight  are  how  many  ? 

73.  Two  and  nine  are  how  many  ? 

74.  Three  and  nine  are   how  many  ? 

75.  Four  and  nine  are  how  many  ? 

76.  Five  and  nine  are  how  many  ? 

77.  Six   and  nine  are  how  many? 

78.  Seven  and  nine  are  how  many  ? 

79.  Eight  and  nine  are  how  many? 

80.  Nine  and  nine  are  how  many? 

81.  Ten  and  nine  are  how  many? 

82.  Two  and  ten  are  how  many? 

83.  Three  and  ten  are  how  many? 

84.  Four  and  ten  are  how  many  ? 

85.  Five  and   ten  are  how  many  ? 

86.  Six  and  ten  are  how  many? 

87.  Seven  and  ten  are  how  many? 

88.  Eight  and  ten  are  how  many? 

89.  Nine  and   ten  are  how  many  ? 

90.  Ten  and  ten  are  how  many  ? 

LESSON  III. 

1.  JOSEPH  bought   three   apples  for  three  cents, 
and  seven  apples  for  seven  cents  ;  how  many  apples 
did  he  buy  ?     How  many  cents  did  he  pay  for  all  the 
apples  ? 

2.  John  bought  three  tops  for  six  cents,  and  Abel 
bought  nine  tops  for  eight  cents  ;  how  many  tops  did 
they  both  buy  ?     How  many  cents  did  they  pay  for 
them  ? 

3.  A  man  bought  three  barrels  of  apples  for  eight 
dollars,  and  twelve  bushels  of  potatoes  for  nine  dollars ; 


14  INTELLECTUAL 


[SEC.  I. 


how  much  did  he  give  for  the  whole  ?     How  much 
less  for  the  apples  than  for  the  potatoes  ? 

4.  A  man  owing  fifteen  dollars,  paid  five  dollars  ; 
how  much  did  he  still  owe  ? 

5.  A  man  owing  fourteen  dollars,  paid  all  but  six 
dollars ;  how  much  did  he  pay  ? 

6.  A  lady  bought  ten   yards  of  ribbon,  and  nine 
yards  of  braid ;  how  many  yards  of  both  did  she  buy  ? 
How  much  more  ribbon  than  braid  ? 

7.  A  man  bought  three  sheep  for  fifteen  dollars,  and 
six  lambs  for  five  dollars ;   how  many  animals  did  he 
buy  ?     How  many  more    lambs   than    sheep  ?     How 
many  dollars  did  he  pay  for  all  ? 

8.  A  boy  bought  sixteen  marbles,  but  lost  five  of 
them ;  how  many  had  he  left  ? 

9.  A  boy  having  eighteen  marble?,  lost  a  part  of 
them,  and  had  twelve  left ;  how  many  did  he  lo^e  ? 

10.  A  man  bought  a  cow    for  twenty  dollars,  but 
could  not  sell  her  for  so  much  by  six  dollars ;  for  what 
sum  could  he  sell  her  ? 

11.  Two  boys,   Richard  and  Martin,  played  at  mar- 
bles.   When  they  began  to  play  they  had  eight  mar- 
bles apiece,  but  when  they  finished  their  game,  Richard 
had  won  three ;  how  many  marbles  had  each  then  ? 

12.  A  man   bought   eighteen  pounds  of  sugar,  and 
lost  six  pounds  of  it  as  he  was  carrying  it  home ;  how 
many  pounds  had  he  left  ? 

13.  A    boy    bought  nineteen   chickens,    and   a  cat 
killed  all  but  ten  of  them  ;  how  many  did  the  cat  kill  ? 

14.  A  merchant  bought  a  firkin  of  butter  for  eigh- 
teen dollars,  but,  it  being  damaged,   he  sold  it  again 
for  fourteen  dollars ;  how  much  did  he  lose  ? 

15.  A  farmer  bought  a  colt  for  fifteen  dollars;  he 
paid  five  dollars  for  keeping  it,  and  then  sold  it  for 
twenty-three  dollars  ;  how  much  did  he  gain  ? 

1 G.  Ten  boys  and  nine  boys  are  how  many  boys  ? 
L  17.  Ten  birds  and  nine  birds  are  how  many  birds  ? 


,ES.  IV.]  ARITHMETIC. 

LESSON  IV. 

1.  Two  and  one  are  how  many? 

2.  Two  and  two  are  how  many  ? 

3.  Four  and  two  are  how  many  ? 

4.  Seven  and  two  are  how  many  ? 

5.  Five  and  two  are  how  many  ? 

6.  Nine  and  two  are  how  many  ? 

7.  Six  and   two   are  how  many  ? 

8.  Eight  and  two   are  how  many  ? 

9.  Three  and  two  are  how  many  ? 

10.  Ten  and  two  are  how  many? 

11.  Two  and  three   are  how  many  ? 

12.  Six  and   three   are  how  many? 

13.  Four  and  three   are  how  many  ? 

14.  Seven  and  three   are  how  many  ? 

15.  Three  and  three   are  how  many? 

1 6.  Five  and   three   are  how  many  ? 

17.  Eight  and   three   are  how  many  ? 

18.  Ten  and  three  are  how  many  ? 

19.  Nine  and  three   are   how  many  ? 

20.  Five  and  four  are  how  many? 

21.  Two  and  four  are   how  many? 

22.  Four  and  four  are  how  many? 

23.  Three  and  four  are  how  many  ? 

24.  Six  and  four  are    how  many? 

25.  Nine  and  four  are  how  many  ? 
2  6.  Seven  and  four  are  how  many  ? 

27.  Ten  and  four   are  how  many  ? 

28.  Eight  and  four  are  how  many  ? 

29.  Two  and   five   are   how  many  ? 

30.  Three  and   six  are  how  many  ? 

31.  Six  and   five  are  how  many  ? 

32.  Seven  and  six  are  how  many  ? 

33.  Nine    and   six  are  how  many  ? 

34.  Eight  and  five  are  how  many  ? 

35.  Five   and  five  are  how  many? 


10  INTELLECTUAL  [SEC.  I. 

36.  Four  and  six  are  how  many  ? 

37.  Six  and  six  are  how  many  ? 

38.  Nine  and  five  are  how  many? 

39.  Eight  and  six  are  how  many? 

40.  Six  and  ten  are  how  many? 

41.  Seven  and  eight  are  how  many? 

42.  Eight  and  nine  are  how  many? 

43.  Ten  and  eight  are  how  many? 

44.  Eight  and  seven  are  how  many? 

45.  Nine  and  nine  are  how  many? 

46.  Ten  and  five  are  how  many? 

47.  Ten  and  seven  are  how  many? 

48.  Nine  and  eight  are  how  many? 

49.  Ten  and  ten  are  how  many  ? 

50.  Three  and  ten  are  how  many? 

51.  Seven  and  seven  are  how  many? 

52.  Five   and  seven  are  how  many  ? 

53.  Nine  and  seven  are  how  many  ? 

54.  Eight  and  eight  are  how  many? 

55.  Three  and  eight  are  how  many? 

56.  Seven  and  ten  are  how  many  ? 

57.  Two  and  ten  are  how  many? 

58.  Four  and  ten  are  how  many? 

59.  Two  and  eight  are  how  many? 

60.  Four  and  seven  are    how  many  ? 

61.  Four  and  eight  are  how  many  ? 

62.  Nine  and  ten  are  how  many  ? 

LESSON  V. 

1.  THREE  less  two  are  how  many? 

2.  Five  less  one  are  how  many? 

3.  Six  less  three  are  how  many? 

4.  Six  less  two  are  how  many  ? 

5.  Seven  less  five  are  how  many? 

6.  Six  less  four  are  how  many? 

7.  Eight  less  three  are  how  many? 


LES.  V.]  ARITHMETIC.  17 

8.  Eight  less  five  are  how  many  ? 

9.  Nine  less  one  are  how  many? 

1 0.  Nine  less  five  are  how  many  ? 

11.  Five  less  three  are  how  many? 

12.  Nine  less  three  are  how  many  ? 

13.  Ten  less  two  are  how  many  ? 

14.  Eight  less  six  are  how  many  ? 

15.  Eight  less  two  are  how  many? 

16.  Ten  less  seven  are  how  many? 

17.  Eleven  less  ten  are  how  many  ? 

18.  Eleven  less  six  are  how  many? 

19.  Ten  less  five  are  how  many? 

20.  Ten  less  nine  are  how  many  ? 

21.  Twelve  less   six  are   how  many? 

22.  Twelve  less  nine  are  how  many  ? 

23.  Eight  less  four  are  how  many? 

24.  Thirteen  less   six  are  how   many  ? 

25.  Thirteen  less  two  are   how  many? 

26.  Fifteen  less  ten  are  how  many  ? 

27.  Twenty  less  ten   are  how  many? 

28.  Sixteen  less  six  are  how  many  ? 

29.  Sixteen  less  ten  are  how  many  ? 

30.  Fifteen  less  four  are  how  many? 

31.  Eighteen  less  eight  are  how  many  ? 

32.  Eighteen  less  ten  are  how   many? 

33.  Nineteen  less  one  are  how  many  ? 

34.  Seventeen  less  three  are  how  many  ? 

35.  Seventeen  less  ten  are  how  many  ? 

36.  Eighteen   less  six  are  how  many? 

37.  Nineteen  less  nine  are  how  many? 

38.  Twenty  less  five  are  how  many  ? 

39.  Twenty-five  less  five  are  how  many  ? 

40.  Twenty-six  less  three  are  how  many  ? 

41.  Eight  and  six,   less  four,  are  how  many  ? 

42.  Ten  and  eight,  less  six,  are  how  many  ? 

43.  Four  and  nine,  less   seven,  are  how  many  ? 

44.  Sixteen  and   six,  less   two,  are  how  many  ? 


18  INTELLECTUAL  [SEC.  I 

LESSON  VI. 

1.  TRREE  boys,  James,  William,  and  George,  wen* 
a  fishing.     James  caught  six  fishes,  William  caught 
four,  and  George  caught  three  ;  how  many  did  they 
all  catch  ?     How  many  more  did  James  catch  than 
George  ? 

2.  Three  girls,  Mary,  Ella,  and  Frances,  gave  some 
flowers  to  their  teacher.     Mary  gave  her  seven  ;  Ella, 
three  ;  and  Frances,  four :  how  many  flowers  did  the 
teacher  receive  ?     How  many  less  did  Ella  give  than 
Mary  ? 

3.  Joseph  had  seven  peaches ;  David,  seven ;  and 
Thomas,  nine.     Joseph  gave  two  to  George,  David 
gave  him  three,  and  Thomas  gave  him  one  ;  how  many 
peaches  did  each  of  the  boys  then  have  ? 

4.  A  boy  gave  live  apples  to  one  of  his  companions  ; 
to  another,   eight ;  to  another,  three  ;  and  kept  four 
himself:  how  many  had  he  at  first  ? 

5.  A  generous  boy  having  eighteen  peaches,  gave 
three  of  them  to  one  companion,  six  to  another,  and 
five  to  another  ;  how  many  did  he  give  away  ?     How 
many  did  he  keep  ? 

6.  A  man  paid  three  dollars  for  some  sugar,   six 
dollars  for  two  barrels  of  apples,  ten  dollars  for  a  bar- 
rel of  flour,  and  had  six  dollars  left ;  how  many  dollars 
had  he  at  first  ? 

7.  A  boy  having  twenty-five  cents,  paid  ten  cents 
for  a  melon,  four  cents  for  an  orange,  and  gave  away 
six  cents  ;  how  many  cents  had  he  remaining  ? 

8.  A  boy  bought  a  ball  for  sixteen  cents ;  he  gave 
ten  cents  to  have  it  covered,  and  then  sold  it  for  thirty- 
two  cents  ;  how  much  did  he  gain  by  the  bargains  ? 

9.  A  man  bought  a  cow  for  eighteen  dollars ;  he 
paid  nine  dollars  for  pasturing  her,  and  then  sold  her 
for  twenty-five  dollars  ;  how  much  did  he  lose  by  the 
bargains  ? 


LES.  VII.]  ARITHMETIC.  10 

10.  A  tailor  bought  some  cloth  for  fifteen  dollars ;  he 
paid  seven  dollars  to  have  it  made  into  a  coat,  and 
then  sold  the  coat  for  twenty-seven  dollars ;  how  much 
did  he  gain  on  the  coat  ? 


LESSON  VII. 

1.  IF  one  lemon  is  worth  two  cents,  what  are  two 
lemons  worth  ?     What  are  three  worth  ? 

2.  What  cost  two  oranges,  at  three  cents  apiece  ? 

3.  What  cost  four  yards  of  cloth,  at  three  dollars  a 
yard  ?     What  at  four  dollars  a  yard  ? 

4.  There  are  three  feet  in  one  yard ;  how   many 
feet  are  there  in  five  yards  ?     In  six  yards  ?     In  six 
yards  and  one  foot  ?     In  ten  yards  and  two  feet  ? 

5.  Bought  two  oranges  at  five  cents  apiece,  and  four 
lemons  at  three  cents  apiece ;  what  did  I  pay  for  the 
oranges  ?     What  for  the  lemons  ?     For  both  ? 

6.  Sold  seven  barrels  of  apples  at  two  dollars  a  bar- 
rel, and  two  cords  of  wood  at  five  dollars  a  cord ;  how 
many  dollars  did  I  receive  for  the  apples  ?     For  the 
wood  ?     For  both  ? 

7.  What  cost  five  yards  of  ribbon,  at  ten  cents  a 
yard  ?     At  nine  cents  ? 

8.  If  I  recite  three  lessons  each  day,  how  many 
shall  I  recite  in  six  days  ?     In  ten  days  ? 

9.  If  four  bushels  of  wheat  make  a  barrel  of  flour, 
how  many  bushels  will  make  six  barrels  ?    Eight  bar- 
rels? 

10.  What  cost  five  pineapples,  at  ten  cents   each  ? 
At  eight  cents  ? 

1 1 .  What  will  six  barrels  of  flour  cost,  at  eight  dol- 
lars a  barrel  ?     At  ten  dollars  ? 

12  If  a  horse  travel  eight  miles  in  an  hour,  how  far 
will  he  travel  in  seven  hours  ? 

13.  What  cost  ten  pounds  of  sugar,  at  nine  cents  a 
pound  ?  At  ten  c^rits  ? 


20  INTELLECTUAL  [SEC.  I. 

14.  "What  is  the  value  of  nine  dove?,  at  nine  cents 
apiece  ?     At  eleven  cents  ? 

15.  If  a  man  earn  seven  dollars  in  one  week,  how 
much  will  he  earn  in  seven  weeks  ?     In  ten  weeks  ? 


LESSON  VIII. 

1.  Two  times  one  are   how  many? 

2.  Two  times  two   are   how   many? 

3.  Two  times  three   are  how  many  ? 

4.  Two  times  four   are   how  many  ? 

5.  Two  times  five   are  how  many? 

6.  Two  times   six  are   how  many? 

7.  Two  times   seven   are  how  many? 

8.  Two  times  eight  are  how  many  ? 

9.  Two  times  nine  are  how  many  ? 

10.  Two  times   ten   are   how   many  ? 

11.  Two  times  eleven   are   how   many? 

12.  Two  times   twelve   are   how   many  ? 

13.  Three  times  one  are  how  many? 

14.  Three  times  two  are  how  many  ? 

15.  Three  times  three  are  how  many  ? 

1 6.  Three  times  four  are   how  many  ? 

17.  Three    times  five   are  how  many? 

18.  Three  times  six  are  how  many? 

19.  Three  times  seven  are  how  many? 

20.  Three  times  eight  are  how  many? 

21.  Three   times  nine  are  how  many? 

22.  Three   times  ten  are  how  many? 

23.  Three  times  eleven  are  how  many  ? 

24.  Three  times  twelve  are  how  many  ? 

25.  Four  times  one  are  how  many  ? 

26.  Four  times   two  are  how  many  ? 

27.  Four  times  three  are  how  many? 

28.  Four  times  four  are  how  many  ? 

29.  Four  times  five   are   how  many  ? 
DO.   Four  times  six   are   how  many  ? 


ARITHMETIC. 


21 


3 1 .  Four  times  seven  arc  how  many  ? 

32.  Four  times   eight  are   how  many? 

33.  Four  times   nine  are   how  many  ? 

34.  Four  times   ten  are  how  many  ? 

35.  Four  times  eleven  are  how  many  ? 

36.  Four  times  twelve  are  how  many  ? 

37.  Five  times  one  are  how  many? 

38.  Five  times  two  are  how  many  ? 

39.  Five  times  three  are  how  many  ? 

40.  Five  times  four  are  how  many  ? 

41.  Five  times  five  are   how  many  ? 

42.  Five  times  six  are  how  many? 

43.  Five  times  seven  are  how  many? 

44.  Five  times  eight  are  how  many? 

45.  Five  times  nine  are  how  many? 

46.  Five  times  ten  are  how  many  ? 

47.  Five  times  eleven  are  how  many  ? 

48.  Five  times  twelve  are  how  many  ? 

49.  Six  times  one  are  how  many  ? 

50.  Six  times   two  are  how  many? 

51.  Six  times  three  are  how  many  ? 

52.  Six  times  four  are  how  many  ? 

53.  Six  times  five  are  how  many  ? 

54.  Six  times  six  are  how  many  ? 

55.  Six  times  seven  are  how  many? 

56.  Six  times   eight  are   how  many  ? 

57.  Six  times   nine  are  how  many  ? 

58.  Six  times  ten  are   how  many  ? 

59.  Six  times  eleven  are  how  many? 
GO.  Six  times  twelve   are   how  many  ? 

61.  Count  to  fifty,  by  twos,  using  the  even  num- 
bers ;  thus,  two,  four,  six,  eight,  etc. 

62.  Count  backward,  by  twos,  from  fifty ;  thus,  fifty, 
forty-eight,  forty-six,  etc. 

63.  Count   by  twos   to  forty-nine,  using   the    odd 
numbers ;  thus,  one,  three,  five,  etc. 

64.  Count  backward,  by  two-,  from  forty-nine  ;  thus, 
forty-nine,  forty -seven,  forty-five,  etc. 


22  INTELLECTUAL  [SEC.  I. 


LESSON  IX. 

!         1.  Two   and  three,  less  one,  are  how  many  ? 

2.  Five   and  four,   less  three,   are  how  many  ? 

3.  Ten  and  two  and  one,  less  five,  are  how  many  ? 

4.  Six  and  ten  and  two,  less  eight,  are  how  many  ? 

5.  Three   times   six,  less  four,  are  how  many? 

6.  Four  times  five,  less  nine,  are  how  many  ? 

7.  Eight  times  two,  less  ten,  are  how  many  ? 

8.  Three   and  six,  less  four,  are  how  many  ? 

9.  Five  times  five,  less  five,  are  how  many  ? 

10.  Six  times  six,  less   six,  are  how  many? 

11.  Six  times  six,  and  six,   are  how  many  ? 

12.  Ten  times  two,  less  six,  are  how  many  ? 

13.  Five  times  six,  and  seven,  are  how  many  ? 

14.  Eight  and  six  and  two,  less  ten,  are  how  many  ? 

15.  Ten  and  six  and  five,  less  nine,  are  how  many  ? 

16.  Ten  times  two,  less  eight,  are  how  many? 

17.  Ten  and  five,  less  nine,  are  how  many? 

18.  Ten  and  eight,  less  six,  are  how  many  ? 

19.  Ten  and  ten,  less  five,  are  how  many? 

20.  Sold  a  sheep   for  six  dollars  and  a  shote  for 
ten  dollars,  and  afterward  paid  three  dollars  for  a  pig ; 
how  many  dollars  had  I  then  ? 

21.  Nellie  found  six  peaches  on  one  tree  and  eight 
on  another,  but  she  has  eaten  two  and  given  three  to 
Jane ;  how  many  has  she  remaining  ? 

22.  A  boy  walked  from  home  twelve  miles  on  one 
day,    and  ten  miles    on   the    next  day,   but  on  the 
third  day  he  returned   seven  miles  ;    how  far  from 
home  was  he  then  ? 

23.  Samuel  had  forty  cents,  but  he  has  given  five 
of  them  for  a  ball,  and  three  for  an  orange  ;  how  many 
cents  has  he  now  ? 

24.  Daniel  sold  six  doves  at  twelve  cents  apiece, 
and  bought  five  chickens  at  ten  cents  apiece ;    how 
much  money  had  he  left  ? 


LES.  X.I  ARITHMETIC.  23 

25.  Thomas  sold  five  melons,  at  ten  cents  each,  and 
paid  twenty-five  cents  for  a  book,  and  ten  cents  for  a 
slate ;  how  many  cents  had  he  remaining  ? 

2G.  A  man  having  fifty  dollars,  paid  twenty  dollars 
for  a  coat,  six  dollars  for  a  pair  of  pantaloons,  and  four 
dollars  for  a  vest ;  how  many  dollars  had  he  left  ? 

27.  A  boy  found  fourteen  eggs  in  one  nest,  and 
eight  less  in  another ;  how  many  eggs  did  he  find  in 
the  second  nest  ?  How  many  in  both  nests  ? 

LESSON  X. 

1.  IF  two  lambs  cost   six  dollars,  what  will   one 
lamb  cost  ? 

2.  How  many   peaches,   at  two  cents   apiece,  can 
you  buy  for  six  cents  ? 

3.  If  I  walk  four   miles  per  hour,  in   how  many 
hours  shall  I  walk  eight  miles  ? 

4.  If  I  walk  eight  miles  in  two  hours,  how  many 
miles  do  I  walk  in  one  hour  ?     How  many  miles  in 
three  hours  ? 

5.  At  three  dollars   a  yard,  how  many  yards  of 
cloth  can  I  buy  for  nine  dollars  ?     For  twelve  dollars  ? 

6.  If  you  pay  twelve  dollars    for    four   yards  of 
cloth,  what  is  the  price  of  one  yard  ? 

7.  Twelve   apples  were    divided   equally  between 
three  boys  ;  how  many  apples  did  each  boy  receive  ? 

8.  In  a  certain  orchard  there  are  fifteen  trees  stand- 
ing in  rows,  and  there  are  five  trees  in  each  row ;  how 
many  rows  are  there  ? 

9.  I  have  twenty  trees,  standing  in  four  equal  rows ; 
how  many  trees  are  there  in  each  row  ? 

10.  How  many  barrels  of  apples,  at  three  dollars  a 
barrel,  can  I  buy  for  fifteen  dollars  ?     For  eighteen 
dollars  ? 

11.  How  many  pears,  at  two  cents  apiece,  can  you 
buy  for  eighteen  cents  ?     For  twenty  cents  ? 


24  INTELLECTUAL  [SEC.  I. 

12.  How  many  oranges,  at  four  cents  apiece,  can 
you  buy  for  twenty  cents  ?     For  twenty-four  cents  ? 

13.  Bought  four  barrels  of  flour  for  twenty-eight 
dollars  ;  what  was  the  price  of  one  barrel  ? 

14.  Paid  twenty-five  cents  for  five  oranges;  how 
many  cents  did  I  pay  for  one  orange  ?     For  two  ? 

15.  How  many  spools  of  thread,  at  eight  cents  a 
spool,  can  be  bought  for  thirty-two  cents  ?     For  forty 
cents  ? 

1 6.  Paid  thirty-six  cents  for  six  spools  of  thread  ; 
how  many  cents  did  I  pay  for  one  spool  ?     For  four  ? 

17.  A  farmer  sowed  twenty-eight  bushels  of  oats 
on  seven   acres  of  land  ;  how  many  bushels  did  he 
sow  on  one  acre  ?     On  five  acres  ? 

18.  If  I  pay  thirty-five  dollars  for  five  cords  of  wood, 
what  is  the  price  of  one  cord  ? 

19.  If  coal  is  worth  six  dollars   a  ton,  how  many 
tons  can  I  buy  for  forty-two  dollars?     For  twenty- 
four  dollars  ? 

20.  If  a  bird  can  fly  twelve  miles  in  one  hour,  in 
what  time  can  it  fly  twenty-four  miles  ?     Thirty-six 
miles  ? 

21.  If  wood  is  worth  six  dollars  a  cord,  and  coal  is 
worth  eight  dollars   a  ton,  how  many  cords  of  wood 
will  pay  for  three  tons  of  coal  ? 

LESSON  XL 

1.  FOUR  are  how  many  times  two? 

2.  Six  are  how  many  times  two  ? 

3.  Six  are  how  many  times  three  ? 

4.  Eight  are  how  many  times  two  ?    Four  ? 

5.  Ten  are   how  many   times  five  ?    Two  ? 
G.  Nine  are    how  many  times   three  ? 

7.  Twelve  are  how  many  times  three  ?    Six? 

8.  Twelve  are  how  many  times  Two  ?    Four  ? 

9.  Fourteen  are  how  many  times  seven  ? 


LES.  XL]  *  ARITHMETIC.  25 

10.  Fifteen  are  how  many  times  five  ?    Three  ? 

11.  Sixteen   are  how   many  times  four  ?   Two  ? 

12.  Eighteen  are   how  many  times  two  ?    Six  ? 

13.  Eighteen  are  how  many  times  three?   Nine? 

14.  Twenty   are  how  many  times  five?    Two? 

15.  Twenty-one  are  how  many  times  seven? 

1 6.  Twenty-four  are  how  many  times  six  ?    Two  ? 

17.  Twenty-four  are  how  many  times  four  ?    Eight  ? 

18.  Twenty-four  are  how  many  times  three? 

19.  Three  times  four  are  how  many  times  three? 

20.  Five  times  eight  are  how  many  times  four  ? 

21.  Six  times  five  are  how  many  times  ten  ? 

22.  Four  times  nine  are  how  many  times  six  ? 

23.  Four  times  six  are  how  many  times  eight  ? 

24.  Ten  times  four  are  how  many  times  eight  ? 

25.  Eight  times  six  are  how  many  times  twelve  ? 

26.  Six  in  twelve,  how  many  times  ? 

27.  Three  in  twenty-one,  how  many  times  ? 

28.  Five  in  thirty-five,  how  many  times  ? 

29.  Eight  in  thirty-two,  how  many  times  ? 

30.  In  forty-two,  how  many  times  six  ? 

31.  In  forty-eight,  how  many  times  eight  ? 

32.  In  thirty-five,  how  many  times  seven  ? 

33.  In  forty-nine,  how  many  times  seven? 

34.  In  fifty,  how  many  times  ten  ?     Five  ? 

35.  Eleven  in  fifty-five,  how  many  times  ? 

36.  Eight  in  fifty-six,  how  many  times  ? 

37.  Twelve  in  sixty,  how  many  times  ? 

38.  Eight  in  seventy-two,  how  many  times  ? 

39.  Nine  in  sixty- three,  how  many  times  ? 

40.  Five  in  fifty-five,  how  many  times  ? 

41.  Eight  times  nine  are  how  many  times  twelve  ? 

42.  Five  times  twelve  are  how  many  times  six  ? 

43.  Three  times  fourteen  are  how  many  times  six  ? 

44.  Three  times  fifteen  are  how  many  times  nine  ? 

45.  Three  times  twenty  are  how  many  times  Iwelve  ? 

46.  Eight  times  nine  are  how  many  times  six? 


26 


INTELLECTUAL 


[SBC.  II. 


SECTION   SECOND. 

LESSON  I. 

REMARKS.  1.  Instead  of  writing  the  names  of 
numbers,  it  is  customary  to  express  them  by  certain 
marks,  or  characters,  called  figures. 

2.  These  figures  are  ten  in  number,  and  are  called 
Arabic  figures. 

3.  Taken  separately,  each  figure  means  the  same  as 
the  word  placed  under  it  in  the  following  lines ;  thus, 

0,        1,     2,      3.       4,       5,      6,      7,        8,       9. 

Naught,  One,  Two,  Three,  Four,  Five,  Six,   Seven,   Eight,  Nine. 

4.  To  express  numbers  greater  than  nine,  these  fig- 
ures are  repeated  and  combined  in  various  ways ;  thus, 


10  . 

....        ten. 

25, 

.     ...  twenty-five. 

11.  . 

.          •     .  eleven. 

26, 

.       twenty-six. 

12.  . 

.     •     .     .  twelve. 

27, 

.  twenty  -seven. 

13,. 
14,. 
15,  . 

.     .     .      thirteen. 
.     .     .     fourteen. 
.   fifteen. 

28, 
29, 
30, 

.     .  twenty-eight. 
.     .    twenty-nine. 
.     .     .    thirty. 

16,. 

...  sixteen. 

31, 

.  thirty-one. 

17,. 

18,. 
19,. 

20,  . 

.     .     .  seventeen. 
.     .     .     eighteen. 
.     .     .    nineteen. 
.     •     •     .  twenty. 

40, 

41, 

90, 
99, 

.     .     .      forty. 
•     .     .     .    forty  -one. 
•     .     .     .     .   ninety. 
.     .     ninety-nine. 

21,. 
22,. 
23,. 
24,. 

.     .      twenty-one. 
.     .     twenty-two. 
.     .  twenty-three. 
.     .    twenty-four. 

100, 
102, 
205, 
900, 

.  one  hundred, 
one  hundred  and  two. 
two  hundred  and  five. 
.     .     .  nine  hundred. 

NOTE.  It  is  presumed  that  the  pupil  is  familiar  with  all  the 
figures,  and  the  manner  of  combining  them  so  as  to  express 
small  numbers,  like  those  in  the  above  Table,  previous  to  study- 
ing this  book.  If,  however,  this  is  found  to  be  untrue  in  any 
case,  such  pupil  should  be  exercised  by  the  teacher,  upon  the 
'  blackboard  or  elsewhere,  until  he  can  readily  write  in  figures 
any  number  less  than  1000. 


LES.  II.]  ARITHMETIC.  27 

5.  To  abbreviate  expressions,  and  to  indicate  the 
relations  of  numbers  to  each  other,  we  sometimes  use 
signs  instead  of  words. 

(5.  This  mark,  $,  is  often  used  as  a  sign  of  the  word 
dollar,  or  dollars  ;  thus,  the  expression  $1,  stands  for 
one  dollar  ;  $4  stands  for  four  dollars. 

7.  The    sign    of   equality,  =,   signifies    that    the 
quantities  between  which  it  stands  are  equal  to  each 
other  ;  thus,  $1  =  100  cents  ;  that  is,  one  dollar  equals 
one  hundred  cents. 

8.  The   sign  of  addition,  -\-,  called  plus   or  and, 
denotes  that  the  quantities  between  which  it  stands 
are  to  be  added  together  ;  thus,  3  -j-  2  =  5  ;  that  is, 
three  plus  two  equals  five,  or  three  and  two  are  five. 

9.  The  sign  of  subtraction, — ,  called  minus  or  less, 
signifies  that  the  number  after  it  is  to  be  taken  from 
the  number  before  it ;  thus,  7  —  4=3;  that  is,  seven 
minus  four,  or  seven  less  four,  equals  three. 

10.  The  sign  of  multiplication,  X?  signifies  that  the 
two  numbers  between  which  it  stands  are  to  be  multi- 
plied together ;  thus,  6  X  5  =  30  ;  that  is,  six  multi- 
plied by  five  equals  thirty,  or  six  times  five  are  thirty. 

11.  The  sign  of  division,  -J-,  indicates  that  the  num- 
ber before  it  is  to  be  divided  by  the  number  after  it ; 
thus,  8  -—  2  =  4 ;  that  is,  eight  divided  by  two  equals 
four,  or  two  in  eight,  four  times. 

LESSON  II. 

1.  MASSACHUSETTS  has  14  counties,  Rhode  Island 
has  5,  and  Connecticut  has  8  ;  how  many  counties  have 
the  three  States  ?     Ans.  14  +  5  -f  8  =  27. 

2.  How    many  more    counties    has    Massachusetts 
than  Rhode  Island  ?     Ans.   14  —  5  =  9. 

3.  If  I  pay  $9  for  a  barrel  of  flour,  $8  for  a  hun- 
dred pounds  of  pork,  and  $3  for  a  bushel  of  beans, 
how  many  dollars  shall  I  pay  for  all  ? 


28 


INTELLECTUAL 


[SEC.  II. 


4.  If  a  ton  of  coal  costs  $8,  and  a  cord  of  wood 
costs  $5,  what  do  they  both  cost  ?     How  much  more 
does  the  coal  cost  than  the  wood  ? 

5.  How  many  are  9  +  8  +  3  ?    9  -—  3  ? 

6.  How  many  are  6  -f-  4  +  7  ?   8  —  5  ? 

7.  How  many  are  7  +  5  +  9  ?    9  —  7  ? 

8.  How  many  are  5  +  8  +  7  ?   7  —  5  ? 

9.  How  many  are  8  -f  6  -f-  7  ?   8  —  6? 

10.  How  many  are  6  -j-  7  +  4  ?    9  —  5  ? 

11.  If  1  barrel  of  flour  costs  $9,  what  will  8  barrels 
cost  ?     Ans.  $9X8=  $72. 

12.  How  many  are  12x5?    11X7? 

13.  How  many  are  6  X  7  ?   9X6? 

14.  How  many  are  10  X  5  ?   8X7? 

15.  How  many  are5xll?    6X12? 

16.  How  many  are  9  X  7  ?   5XH? 

17.  How  many  are  7  X  10  ?    6X8? 

18.  How  many  are  9  X  10  ?    6X7? 

19.  How  many  are  4  X  12  ?    7X8? 

20.  If  8  pounds  of  sugar  cost  72  cents,  what  is  the 
price  of  1  pound?     Ans.  72  cents  -=-  8  =  9  cents. 

21.  How  many  are  56  —  7  ?   63  -4-  9  ? 

22.  How  many  are  32  —  8  ?    24  -*-  6  ? 

23.  How  many  are  40  —  5  ?   42  ~  6  ? 

24.  How  many  are  56  —  8  ?    56  -^-  7  ? 

25.  How  many  are  60  —  10  ?    45  -*-  9  ? 

26.  How  many  are  72  —  12  ?    66  -^  6  ? 

27.  How  many  are  49  —  7  ?   64  -f-  8  ? 

28.  How  many  are  8  —  6  ?   9  +  7  ? 

29.  How  many  are  7X8  —  6?   8X^  +  8? 

30.  How  many  are  48  -f-  4  -f-  3  ?    60  -f- 10  —  2  ? 

31.  How  many  are  9  +  6  +  8  —  3  ?    48  -*-  6  -f  3  ? 

32.  Take  6,  add  4,  multiply  by  2,  divide  by  5,  divide 
by  2,  add  7,  divide  by  3,  multiply  by  4,  subtract  2  ; 
result  ? 

33.  Take  9,  subtract  3,  divide  by  2,  add  5,  multiply 
by  4,  subtract  2,  divide  by  6,  add  7  ;  result  ? 


LES.  III.]  ARITHMETIC.  2'J 

LESSON  III. 

1.  A  MAN  bought  a  tub  of  butter  for  12  dollars, 
and  a  cheese  for  4  dollars  ;  how  many  dollars  did  he 
pay  for  both  ? 

2.  A  farmer  has  8  cows  in  one  pasture,  and  12  in 
another ;   how  many  has  he   in   both  ?     How   many 
more  in  one  than  in  the  other  ? 

3.  George  found   6  marbles,  Arthur  gave  him  10, 
and  he  bought  8  ;  how  many  marbles  had  he  then  ? 

4.  One  morning  Mary  found  in  her  flower-garden 
8  roses,  5  peonies,  7  tulips,  and  10  other  blossoms ; 
she  picked  4  roses,  1  peony,   3  tulips,  and  7   other 
blossoms  ;  how  many  blossoms  did  she  find  ?     How 
many  did  she  leave  in  the  garden  ? 

5.  A  farmer  sold  8  bushels  of  wheat,  9  bushels  of 
corn,  3  bushels  of  rye,  and  7  bushels  of  barley  ;  how 
many  bushels  of  grain  did  he  sell  ? 

6.  A  drover  bought  10  sheep  of  one  man,  7  of  another, 
and  8  of  another,  and  he  afterwards  sold  12  sheep  ; 
how  many  did  he  buy  ?     How  many  did  he  keep  ? 

7.  If  I  earn  12  dollars,  and  spend  7  dollars,  a  week, 
how  many  dollars  shall  I  save  in  a   week  ?     How 
many  in  4  weeks  ? 

8.  Bought  9  yards  of  cloth,  at  4  dollars  a  yard,  and 
sold  the  whole  of  it  for  9  dollars  more  than  I   paid  ; 
what  did  I  receive  for  the  9  yards  ?     What  for  each 
yard  ? 

9.  Bought  8  yards  of  cloth,  at  5  dollars  a  yard,  and 
sold  all  of  it  for  32  dollars  ;  did  I  gain  or  lose  ?     How 
much  on  the  whole  ?     How  much  on  a  yard  ? 

1(X  Mr.  Flint  had  10  sheep  in  each  of  5  pastures, 
but  he  has  sold  5  from  one  pasture,  7  from  another 
and  8  from  another ;  how  many  sheep  has  he  now  ? 

11.  When  flour  is  worth  8  dollars  a  barrel,  and  hay 
12  dollars  a  ton,  how  many  tons  of  hay  will  pay  for  6 
barrels  of  flour  ? 


36  INTELLECTUAL  [-»KC.  II 

12.  In  a  certain  orchard  there  were  7  rows  of  trees, 
and  8  trees  in  each  row,  but  2  trees  have  been  taken 
from  each  row  ;  how  many  trees  still  remain  in  the 
orchard  ? 

13.  Daniel,   Joseph,   and    James   went   a  fishing. 
James  caught  2  fishes,  Joseph  caught  3  times  as  many 
as  James,  and  Daniel  caught  twice  as  many  as  James 
and  Joseph  together ;  how  many  did  Daniel  catch  ? 

14.  Thomas  had  twice  15  peaches,  which  he  divided 
equally  between  his  3  brothers ;  how  many  did   he 
give  to  each  ? 

15.  The  distance  from  Boston  to  Maiden  is  5  miles ; 
from  Maiden  to  Reading,  7  miles;  from  Eeading  ta 
Wilmington,  3  miles ;  from  Wilmington  to  Andover, 
8  miles ;  from  Andover  to  Lawrence,  3  miles  :  how  far 
is  it  from  Boston  to  Lawrence  ? 

16.  The  distance  from  Boston  to  Somerville  is  3 
miles ;  from  Somerville  to  Waltham,  7  rrifteg ;  from 
Waltham  to  Concord,  10  miles ;  from  Concord  to  Little- 
ton, 1 1  miles ;  from  Littleton  to  Groton,  4  miles ;  from 
Groton  to  Fitchburg,  15  miles:  how  far  is  it  from 
Boston  to  Fitchburg  ? 

LESSON  IV. 

THE  following  exercises  are  designed  to  discipline 
the  pupil  in  changing  from  one  subject  to  another 
with  rapidity  and  accuracy. 

Let  the  examples  be  read  across  the  page  ;  thus,  1 
and  1  are  2 ;  1  from  2  leaves  1  ;  once  1  is  1  ;  1  in  1 , 
once  ;  etc.  etc. 

1  and  1  ?  1  from  2  ?  once  1  ?  1  in  1  ? 

1  and  2  ?  1  from  3  ?  once  2  ?  1  in  2  ? 

1  and  3  ?  1  from  4  ?  once  3  ?  1  in  3  ? 

1  and  4  ?  1  from  5  ?  once  4  ?  1  in  4  ? 

1  and  5  ?  1  from  6  ?  once  5  ?  1  in  5  ? 

1  and  6  ?  1  from  7  ?  once  6  ?  1  in  G  ? 


LES.  IV.]  AEITHMETIC.  31 


1  and    7  ? 

1  from    8  ? 

once    7  ? 

1  in    7? 

1  and    8  ? 

1  from    9  ? 

once    8  ? 

1  in    8? 

1  and    9  ? 

1  from  10  ? 

once    9  ? 

1  in    9? 

1  and  10  ? 

1  from  11? 

once  10  ? 

1  in  10  ? 

1  and  11  ? 

1  from  12? 

once  11  ? 

1  in  11  ? 

1  and  12  ? 

1  from  13  ? 

once  12  ? 

1  in  12  ? 

2  and    1? 

2  from    3? 

2  times   1  ? 

2  in    2? 

2  and    2? 

2  from    4? 

2  times  2  ? 

2  in    4? 

2  and    3? 

2  from    5? 

2  times  3  ? 

2  in    6? 

2  and    4? 

2  from    6? 

2  times  4? 

2  in    8? 

2  and    5? 

2  from    7? 

2  times  5  ? 

2  in  10? 

2  and    6? 

2  from    8? 

2  times  6  ? 

2  in  12? 

2  and    7? 

2  from    9? 

2  times  7  ? 

2  in  14? 

2  and    8? 

2  from  10  ? 

2  times  8  ? 

2  in  16? 

2  and    9? 

2  from  11  ? 

2  times   9? 

2  in  18? 

2  and  10? 

2  from  12? 

2  times  10? 

2  in  20  ? 

2  and  11? 

2  from  13? 

2  times  11? 

2  in  22? 

2  and  12  ? 

2  from  14? 

2  times  12? 

2  in  24? 

3  and    1  ? 

3  from    4  ? 

3  times    1? 

3  in    3? 

3  and    2? 

3  from    5? 

3  times    2? 

3in    6? 

3  and    3? 

3  from     6  ? 

3  times   3? 

Sin    9? 

3  and    4? 

3  from    7? 

3  times    4  ? 

3  in  12? 

3  and    5? 

3  from    8? 

3  times    5  ? 

3  in  15? 

3  and    6? 

3  from     9? 

3  times    6? 

Sin  18? 

3  and    7  ? 

3  from  10  ? 

3  times    7? 

3  in  21  ? 

3  and    8  ? 

3  from  11? 

3  times    8? 

3  in  24  ? 

3  and    9  ? 

3  from  12? 

3  times    9? 

3  in  27  ? 

3  and  10  ? 

3  from  13? 

3  times  10  ? 

3  in  30  ? 

3  and  11? 

3  from  14  ? 

3  times  11? 

3  in  33  ? 

3  and  12? 

3  from  15  ? 

3  times  12? 

3  in  36? 

4  and    1? 

4  from    5  ? 

4  times    1  ? 

4  in    4? 

4  and    2? 

4  from    6  ? 

4  times    2? 

4  in    8? 

4  and    3? 

4  from    7? 

4  times    3? 

^  in  12? 

4  and    4  ? 

4  from    8? 

4  times    4  ? 

4  in  16? 

4  and    5? 

4  from    9? 

4  times    5  ? 

4  in  20  ? 

4  and    6  ? 

4  from  10  ? 

4  times    6  ? 

4  in  24? 

32  INTELLECTUAL 


4  and    7? 

4  from  11  ? 

4  times    7  ? 

4  in  28  ? 

4  and    8? 

4  from  12  ? 

4  times    8? 

4  in  32  ? 

4  and    9? 

4  from  13  ? 

4  times    9  ? 

4  in  36? 

4  and  10  ? 

4  from  14  ? 

4  times  10? 

4  in  40  ? 

4  and  11  ? 

4  from  15  ? 

4  times  11? 

4  in  44  ? 

4  and  12?       4  from  16?      4  times  12?      4  in  48? 


LESSON  V. 

1.  How  many  are  nine  and  two  ?     Nineteen  and 
two  ?     Twenty-nine  and  two  ?     Thirty-nine  and  two  ? 
Forty-nine  and  two  ?     Fifty-nine  and  two  ?     Sixty- 
nine  and  two?     Seventy -nine  and  two?     Eighty-nine 
and  two  ?     Ninety -nine  and  two  ? 

2.  How  many  are  nine  and  three  ?     Nineteen  and 
three?      Twenty-nine   and  three?     Thirty-nine  and 
three  ?     Forty-nine  and  three  ?     Fifty-nine  and  three  ? 
Sixty-nine    and    three  ?       Seventy-nine    and    three  ? 
Eighty-nine  and  three  ?     Ninety-nine  and  three  ? 

3.  How  many  are   nine  and  four  ?     Nineteen  and 
four?    Twenty-nine  and  four?     Thirty-nine  and  four  ? 
Forty-nine  and  four  ?     Fifty-nine  and  four  ?     Sixty- 
nine  and  four  ?     Seventy-nine  and  four?    Eighty -nine 
and  four  ?  Ninty-nine  and  four  ? 

4.  How  many  are  nine   and  five  ?     Nineteen   and 
five  ?     Twenty -nine  and  five  ?     Thirty-nine  and  five  ? 
Forty-nine  and  five  ?    Fifty -nine  and  five  ?    Sixty-nine 
and  five  ?     Seventy -nine  and  five  ?     Eighty -nine  and 
five  ?     Ninety-nine  and  five  ? 

5.  How  many  are  nine  and    six  ?    Nineteen    and 
six  ?    Twenty-nine   and   six  ?    Thirty-nine  and   six  ? 
Forty-nine  and  six  ?    Fifty-nine  and  six  ?    Sixty-nine 
and  six?     Seventy -nine  and   six?     Eighty-nine  and 
six  ?     Nj^ety-nine  and  six  ? 

6.  How  many  are  nine  and  seven  ?     Nineteen  and 
seven?      Twenty-nine  and  seven?     Thirty-nine  and 
seven  ?   Forty -nine  and  seven  ?  Fifty-nine  and  seven  ? 


LES.  V.]  ARITHMETIC.  33 

Sixty-nine   and   seven  ?      Seventy-nine   and   seven  ? 
Eigiity-nine  and  seven  ?     Ninety-nine  and  seven  ? 

7.  How  many  are  nine  and  eight  ?    Nineteen  and 
eight  ?     Twenty -nine    and  eight  ?     Thirty-nine   and 
eight  ?    Forty-nine  and  eight  ?    Fifty-nine  and  eight  ? 
Sixty-nine   and    eight  ?      Seventy-nine    and   eight  ? 
Eighty-nine  and  eight  ?    Ninety-nine  and  eight  ? 

8.  How  many  are  nine  and  nine  ?     Nineteen  and 
nine  ?  Twenty-nine  and  nine  ?  Thirty-nine  and  nine  ? 
Forty-nine  and  nine  ?    Fifty-nine  and  nine  ?    Sixty- 
nine  and  nine  ?    Seventy-nine  and  nine  ?   Eighty-nine 
and  nine  ?     Ninety-nine  and  nine  ? 

9.  How  many  are  nine  and  ten  ?     Nineteen  and 
ten  ?     Twenty-nine  and  ten  ?     Thirty-nine  and  ten  ? 
Forty-nine  and  ten  ?    Fifty-nine  and  ten  ?    Sixty-nine 
and  ten  ?  Seventy-nine  and  ten  ?  Eighty-nine  and  ten  ? 
Ninety-nine  and  ten  ? 

10.  How  many  are  eight  and  three  ?  Eighteen  and 
three  ?     Twenty-eight  and  three  ?     Thirty-eight  and 
three  ?   Forty-eight  and  three  ?    Fifty-eight  and  three  ? 
Sixty-eight  and   three  ?      Seventy-eight  and  three  ? 
Eighty-eight   and    three  ?     Ninety-eight  and  three  ? 

11.  How  many  are  eight  and  four  ?     Eighteen  and 
four  ?     Twenty-eight   and   four  ?      Thirty-eight   and 
four  ?     Forty-eight  and  four  ?     Fifty-eight  and  four  ? 
Sixty-eight    and    four?      Seventy-eight    and    four? 
Eighty-eight  and  four  ?     Ninety-eight  and  four  ? 

12.  How  many  are  eight  and  five?     Eighteen  and 
five  ?    Twenty-eight  and  five  ?  Thirty-eight  and  five  ? 
Forty-eight  and  five  ?     Fifty-eight  and  five  ?     Sixty- 
eight  and  five  ?  Seventy-eight  and  five  ?  Eighty-eight 
and  five  ?     Ninety-eight  and  five  ? 

13.  How  many  are  eight  and  six  ?     Eighteen  and 
six  ?     Twenty-eight  and  six  ?     Thirty-eight  and  six  ? 
Forty-eight  and  six  ?     Fifty-eight  and  six  ?     Sixty- 
eight  and  six  ?    Seventy-eight  and  six  ?    Eighty-eight 
and  six  ?     Ninety-eight  and  six  ? 


34  INTELLECTUAL  [SEC.  II. 

14.  How  many  are   eight  and  seven?     Eighteen 
and  seven  ?     Twenty-eight  and  seven  ?     Thirty-eight 
and  seven  ?    Forty-eight  and  seven  ?    Fifty-eight  and 
seven?     Sixty-eight  and  seven?     Seventy -eight  and 
seven  ?     Eighty-eight  and  seven  ?     Ninety-eight  and 
seven  ? 

15.  How  many  are  eight  and  eight  ?   Eighteen  and 
eight  ?   Twenty-eight    and   eight  ?    Thirty-eight   and 
eight  ?    Forty-eight  and  eight  ?    Fifty-eight  and  eight  ? 
Sixty-eight   and  eight  ?     Seventy -eight    and   eight  ? 
Eighty-eight  and  eight  ?    Ninety-eight  an.d  eight  ? 

16.  How  many  are  eight  and  nine  ?     Eighteen  and 
nine  ?     Twenty-eight  and   nine  ?      Thirty-eight  and 
nine  ?     Forty-eight  and  nine  ?     Fifty-eight  and  nine  ? 
Sixty-eight    and    nine  ?     Seventy-eight    and    nine  ? 
Eighty-eight  and  nine  ?     Ninety-eight  and  nine  ? 

17.  How  many  are  eight  and  ten  ?     Eighteen  and 
ten  ?     Twenty-eight  and  ten  ?     Thirty-eight  and  ten  ? 
Forty-eight  and  ten  ?     Fifty-eight  and  ten  ?     Sixty- 
eight  and    ten  ?     Seventy-eight   and   ten  ?     Eighty- 
eight  and  ten  ?     Ninety-eight  and  ten  ? 

LESSON  VI. 

1.  A  MAN  bought  a  eow  for  28  dollars,  a  sheep  for 
10  dollars,  and  a  calf  for  6  dollars ;  how  much  did  he 
pay  for  all  ? 

2.  A  farmer  sold  a  tub  of  butter  for  19  dollars, 
some  cheese  for  9  dollars,  and  3  barrels  of  apples  for 
6  dollars ;  how  much  did  he  receive  for  all  ? 

3.  A  drover  bought  48  sheep  of  one  man,  10  of 
another,  and  7  of  another ;   how  many   sheep  did  he 
buy? 

4.  A  boy  gave  39  cherries  to  one  of  his  companions, 
9  to  another,  and  3  to  another ;  how  many  cherries  did 
he  give  away  ? 

5.  Bought  a  piece  of  land  for  79  dollars,  another 


LES.  VII.]  ARITHMETIC.  So 

piece  for  10  dollars,  and  another  for  9  dollars ;  what 
did  I  pay  for  the  whole  ? 

6.  A  grocer  bought  4  barrels  of  flour  for  28  dollar?, 
20   bushels  of  oats   for  10    dollars,   and  a   hundred 
weight  of  sugar  for  9  dollars ;  what  did  he  pay  for  the 
whole  ? 

7.  How  many  are  forty-eight  and  ten  and  six  ? 

8.  How  many  are  seventy  and  nine  and  six  ? 

9.  How  many  are  fifty-eight  and  ten,  less  six  ? 

10.  Mr.  Smith   bought  a  horse  for  69  dollars,  and 
paid  10  dollars  for    keeping  him  and   3   dollars  for 
shoeing  him.     He  let  the  horse  go  on  a  journey,  for 
which  he  received  12  dollars,  and  then  sold  him  fur 
75  dollars ;  how  much  did  he  gain  ? 

11.  A  man  bought  a  piece  of  land  for  89  dollars,  and 
paid  9  dollars  for  plowing  a  part  of  it,  and  10  dollars 
for  fencing  it.  He  received  15  dollars  for  the  grass  that 
grew  on  it,  and  then  sold  it  for  100  dollars ;  how  much 
did  he  gain  ? 

LESSON  VJL 

1 .  How  many  are  7  and  4  ?  1 7  and  4  ?  27  and  4  ? 
37  and  4?  47  and  4?  57  and  4  ?  G7  and  4?  77 
and  4?  87  and  4  ?  97  and  4? 

2.  How  many  are  7  and  5  ?  17  and  5  ?  27  and  5  ? 
37  and  5?  47  and  5  ?  57  ^nd  5?  G7  and  5  ?  77 
and  5?  87  and  5?  97  and  5  ? 

3.  How  many  are  7  and  6  ?  17  and  6  ?  27  and  6  ? 
37  and  6?  47  and  6?  57  and  6?  G7  and  G?  77 
and  6  ?  87  and  G  ?  97  and  6  ? 

4.  How  many  are  7  and  7  ?  17  and  7  ?  27  and  7  ? 
37  and  7  ?  47  and  7  ?  57  and  7  ?  G7  and  7  ?  77 
and  7  ?  87  and  7  ?  97  and  7  ? 

5.  How  many  are  7  and  8  ?  17  and  8  ?  27  and  8  ? 
37  and  8  ?  47  and  8  ?  57  and  8  ?  67  and  8  ?  77  and 
8  ?  87  and  8  ?  97  and  8  ? 


36  INTELLECTUAL  [SEC.  II. 

6.  How  many  are  7  and  9  ?  17  and  9  ?  27  and  9  ? 

37  and  9  ?  47  and  9  ?  57  and  9  ?  67  and  9  ?  77  and 

9  ?  87  and  9  ?  97  and  9  ? 

7.  How  many  are  7  and  10?  17  and  10?  27  and 
10?  37  and  10?  47  and  10?  57  and  10?  67  and 

10  ?  77  and  10  ?  87  and  10  ?  97  and  10  ? 

8.  How  many  are  6  and  5  ?  16  and  5  ?  26  and  5  ? 
36  and  5  ?  46  and  5  ?  56  and  5  ?  66  and  5  ?  76  and 

5  ?  86  and  5?  96  and  5  ? 

9.  How  many  are  6  and  6  ?    16  and  6  ?    26  and  6  ? 
36  and  6  ?    46  and  6  ?    56  and  6  ?    66  and  6  ?   76  and 
6?   86  and  6?    96  and  6? 

10.  How  many  are  6  and  7  ?    16  and  7  ?    26  and  7  ? 
36  and  7?   46  and  7  ?    56  and  7?    66  and  7?    76  and 
7?    86  and  7  ?    96  and  7  ? 

11.  How  many  are  6  and  8  ?    16  and  8  ?    26  and  8  ? 
36  and  8  ?    46  and  8  ?    56  and  8  ?    66  and  8  ?   76  and 
8?   86  and  8  ?   96  and  8  ? 

12.  How  many  are  6  and  9  ?    16  and  9  ?    26  and  9  ? 
36  and  9  ?    46  and  9  ?    56  and  9  ?    66  and  9  ?   76  and 
9?   86  and  9?    96  and  9? 

13.  How  many  are  6  and  10  ?    16  and  10  ?    26  and 
10?   36  and  10?    46  and  10?    56  and  10?    66  and  10? 
76  and  10?    86  and  10  ?    96  and  10? 

14.  How  many  are  5  and  6  ?    15  and  6  ?    25  and  f>  ? 
35  and  6?    45  and  6  ?    55  and  6?   65  and  6?    75  and 

6  ?   85  and  6  ?    95  and  6  ? 

15.  How  many  are  5  and  7  ?  15  and  7  ?  25  and  7  ? 
35  and  7  ?  45  and  7  ?  55  and  7  ?  65  and  7  ?  75  and 

7  ?  85  and  7  ?  95  and  7  ? 

16.  How  many  are  5  and  8  ?  15  and  8  ?  25  and  8  ? 
35  and  8  ?  45  and  8  ?  55  and  8  ?  65  and  8  ?  75  and 

8  ?  85  and  8  ?  95  and  8  ? 

17.  How  many  are  5  and  9  ?  15  and  9?  25  and  9  ? 
35  and  9  ?  45  and  9  ?  55  and  9  ?  65  and  9  ?  75  and 

9  ?  85  and  9  ?  95  and  9  ? 

18.  How  many  are  5  and  10  ?    15  and  10  ?    25  and 


LES.  VIIL]  ARITHMETIC.  37 

10?    35  and  10?   45  and  10?    55  and  10?    65  and 
10  ?    75  and  10  ?    85  and  10  ?    95  arid  10  ? 

19.  How  many  are  4  and  7  ?    14  and  7  ?    24  and  7  ? 
34  and  7  ?    44  and  7  ?    54  and  7  ?    64  and  7  ?    74  and 

7  ?  84  and  7  ?    94  and  7  ? 

20.  How  many  are  4  and  8  ?    14  and  8  ?    24  and  8  ? 
34  and  8?   44  and  8?    54  and  8  ?    64  and  8?    74  and 
8?    84  and  8?   94  and  8  ? 

21.  How  many  are  4  and  9  ?    14  and  9?    24  and  9  ? 
34  and  9  ?   44  and  9  ?   54  and  9  ?    64  and  9  ?   74  and 

9  ?   84  and  9  ?    94  and  9  ? 

22.  How  many  are  4  and  10  ?    14  and  10  ?    24  and 
10?    34  and  10?    44  and  10?   54  and  10?    64  and 

10  ?   74  and  10  ?    84  and  10  ?    94  and  10  ? 

23.  How  many  are  3  and  8  ?    13  and  8  ?   23  and  8  ? 
33  and  8  ?   43  and  8  ?    53  and  8  ?    63  and  8  ?   73  and 

8  ?   83  and  8  ?    93  and  8  ? 

24.  How  many  are  3  and  9  ?  13  and  9  ?  23  and  9  ? 
33  and  9  ?  43  and  9  ?  53  and  9  ?  63  and  9  ?  73  and 

9  ?  83  and  9  ?  93  and  9  ? 

25.  How  many  are  3  and  10?  13  and  10?  23  and 
10?  33  and  10?  43  and  10?  53  and  10?  63  and 

10  ?  73  and  10  ?  83  and  10  ?  93  and  10  ? 

26.  How  many  are  2  and  9  ?  12  and  9  ?  22  and 

9  ?  32  and  9  ?  42  and  9  ?  52  and  9  ?  62  and  9  ? 
72  and  9  ?  82  and  9  ?  92  and  9  ? 

27.  How  many  are  2  and  10  ?  12  and  10  ?  22  and 

10  ?  32  and  10  ?  42  and  10  ?  52  and  10  ?  62  and 
10  ?  72  and  10  ?  82  and  10  ?  92  and  10  ? 


LESSON  VIIL 

1.  THOMAS  paid  33  cents  for  an  arithmetic,  9  cents 
for  a  writing-book,  and  8  cents  for  some  ink ;  how 
niJiny  cents  did  he  pay  for  all  ? 

2.  Abel  bought  a  knife  for  75  cents,  a  top  for  10 
cents,  and  a  ball  for  6  cents  ;  what  did  he  pay  for  all  ? 


38  INTELLECTUAL  [SEC.  II. 

3.  Thirty-seven  apples  are  growing  on  one  branch, 
8  on  another,  9  on   another,  6  on   angther,  and  9  on 
another ;  how  many  apples  are  growing  on  the  five 
branches  ? 

4.  Twenty-five  peaches  were  growing  on  one  tree, 
6  on  another,  and  9  on  another ;  but  10  have  been 
picked  from  the  first  tree,  and  5  from  the  third  ;  how 
many  peaches  remain  on  the  three  trees  ? 

5.  How  many  are  26  and  8  and  9  and  7,  less  5  ? 

6.  A  poor  woman  bought  a  pound  of  cheese  for  9 
cents,  a  pound  of  crackers  for  8  cents,  and  3  pounds 
ef  sugar  at  1 1  cents  a  pound ;  how  many  cents  did 
she  pay  for  all  ? 

7.  A  merchant  sold  6  barrels  of  flour  at  8  dollars 
a  barrel,  and  took  his  pay  in  hay  at  12  dollars  a  ton  ; 
how  many  tons  did  he  receive  ?     . 

8.  A  farmer  has  15  acres  of  corn,  8  acres  of  wheat, 
5  acres  of  rye,  and  9  acres  of  oats ;  how  many  acres 
of  grain  has  he  ? 

9.  A  drover  bought  27  cows  of  one  man,  9  of  an- 
other, 6  of  another,  and  8  of  another.     He  afterwards 
sold  10  of  them  ;  how  many  had  he  then  ? 

10.  A   sportsman    caught    23    squirrels,  3  foxes,  8 
rabbits,  10  woodchucks,  and  9  birds  ;  how  many  ani- 
mals did  he  catch  ? 

11.  In  a  certain  orchard  there  are  43  apple  trees, 
10  peach  trees,  7  pear  trees,  8  cherry  trees,  and  6  quince 
trees ;  how  many  trees  are  there  in  the  orchard  ? 

12.  A  lady  bought  a  silk*  dress  for  22  dollars,  a 
bonnet  for  9  dollars,  a  shawl  for  6  dollars,  a  pair  of 
shoes  for  2  dollars,  a  pair  of  gloves  for  1  dollar,  and 
had   10  dollars   left ;    how  many  dollars   had  she  at 
first? 

13.  A  man  paid  75  dollars  for  a  horse,  9  dollars  for 
a  saddle,  3  dollars  for  a  bridle,  and  1  dollar  for  a  whip  ; 
what  did  they  all  cost  him  ? 

11.  A  miller  bought  54  bushels  of  wheat,  10  of  rye, 


LES.  EX.]  ARITHMETIC*  #9 

8  of  corn,  and  3  of  buckwheat ;  how  many  bushels  of 
grain  did  he  buy  ? 

15.  David  has  37  cents  in  his  purse,  8  in  one  pocket, 

9  in  another  pocket,  and  seven  in  his  hand ;  how  many 
cents  has  he? 

16.  James  had  37  cents,  and  George  gave  him  7, 
Charles  6,  Samuel  9,  John  8,  and  he  bought  a  top  for 

10  cents  ;  how  many  cents  had  he  left? 

17.  A  lady  gave  50  dollars  for  a  watch,  9  dollars 
for  a  chain,  1  dollar  for  a  key,  and  5  dollars  for  a  pin ; 
how  many  dollars  did  she  give  for  all  ? 

18.  How  many  are  54  and  10  and  8  and  6,  less  9  ? 

19.  How  many  are  83  and  7  and  9  and  5  and  3, 
less  8? 

LESSON  IX. 

1.  How  many  are  11  less  2  ?    21  less  2  ?    31  less 
2?   41  less  2  ?   51  less  2?   61  less  2  ?   71  less  2?   81 
less  2?    91  less  2?    101  less  2? 

2.  How  many  are  11  less  3  ?    21  less  3?    31  less 
3?   41  less  3?   51  less  3?   61  less  3  ?   71  less  3?   81 
less  3?   91  less  3?    101  less  3? 

3.  How  many  are  11  less  9  ?    21  less  9  ?    31  less 
9  ?   41  less  9  ?   51  less  9  ?   61  less  9  ?   71  less  9  ?  81 
less  9  ?   91  less  9  ?    101  less  9  ?. 

4.  How  many  are  12  less  5  ?    22  less  5  ?    32  less 
5?   42  less  5?   52  less  5  ?    62  less  5  ?   72  less  5?   82 
less  5  ?   92  less  5  ?   102  less  5  ? 

5.  How  many  are  14  less  8  ?    24  less  8  ?    34  less 
8  ?  44  less  8  ?   54  less  8  ?  64  less  8  ?   74  less  8  ?   84 
less  8  ?   94  less  8  ?    104  less  8  ? 

6.  Thirty-six  and  9  and  4  and  8,  less  7,  are  how 
many  ? 

7.  Forty-four  and  2  and  7  and  9  and  3  and  8  and 
5,  less  6,  are  how  many  ? 

8.  Fifty-nine  and  5  and  6  and  7  and  3  and  8  and 
4,  less  2,  are  how  many  ? 


40  INTELLECTUAL  [SEC.  II. 

9.  Sixteen  and  4  and  10  and  12  and  8  and  3  and 
9,  less  7,  are  how  many  ? 

10.  Eighty-one  and  9  and  10  and  3  and  8  and  6,  less 
7,  are  how  many  ? 


LESSON  X. 

1.  WHAT  cost  9  yards  of  cloth,  at  $4  a  yard? 

2.  What   cost  8   pounds    of  sugar,   at   9    cents   a 
pound  ? 

3.  What  cost  6  dozen  of  eggs,  at  12  cents  a  dozen  ? 

4.  A  and  B  start  from  the  same  place  and  travel 
in  the  same   direction.  A-  at  the   rate   of  9  miles  an 
hour  and  B  6  miles ;  how  far  apart  are  they  in  1  hour? 
In  5  hours?    In  8  hours?    10  hours?     12  hours?   20 
hours  ? 

5.  A  and  B  start  from  the  same  place  and  travel 
in   opposite  directions,  A  at    the  rate  of  5  miles  an 
hour,  and   B   4  miles  ;  how   far   apart  are   they  in  1 
hour  ?    In  6  hours  ?    9  hours  ?     10  hours  ?    12  hours  ? 

6.  A  man  bought  9  yards  of  cloth,  at  5  dollars  a 
yard,  for  a  suit  of  clothes,  and  paid  6  dollars  for  mak- 
ing the  coat,  2  dollars  for  making  the  pantaloons,  and 
1  dollar  for  making  the  vest  ;  what  did  the  suit  cost  ? 

7.  At  9  cents  each,  what  will  6  pineapples  cost? 

8.  At  5  dollars  a  pair,   what  will  9  pair  of  boots 
cost?    6  pair?     10  pair  ?     12  pair? 

9.  In  my  garden   there  are  7  rows  of  corn,  and  9 
hills  in  each  row ;  how  many  hills  of  corn  are  there  in 
the  garden? 

10.  In  1  bushel  there  are  4  pecks  ;  how  many  pecks 
are  there  in  3  bushels  ?    In  5  bushels  ? 

11.  How  many  pecks  are  there  in  5  bushels  and  1 
peck  ?    In  5  bushels  and  3  peeks  ? 

12.  In  1  peck  there  are  8  quarts;  how  many  quarts 
are  there  in  4  pecks  ?    Then  how  many  quarts  are  there 
in  1  bushel  ?     Why  ? 


S.  XI^ 


LES.  XI.]  ARITHMETIC.  41 

13.  How  many  quarts  are  there  in  1  bushel  and  1 
peck  ?     How  many  in  1  bushel  and  2  pecks  ?     How 
many  in  1  bushel,  3  pecks,  and  2  quarts  ? 

14.  Count  by  twos  from  50  to  100;  thus,  50,  52, 

54,  etc. 

15.  Count  backward  from  100  thus :  100,  98,  96,  etc. 

16.  Count  by  twos  from  51  to  101 ;  thus,  51,  53, 

55,  etc. 

17.  Count   backward    from   101    thus  :    101,   99, 
97,  etc. 

18.  Count  by  threes  to  99  ;  thus,  3,  6,  9,  etc. 

19.  fcount  backward  from  99  thus:  99,  96,  93,  etc. 

20.  Count  by  threes  from  1  to  100 ;  thus,  1,  4,  7, 
10,  etc. 

21.  Count  backward  from  100  thus :  100,  97,  94,  etc. 

22.  Count  by  threes  from  2  to  101 ;  thus,  2,  5,  8,  etc. 

23.  Count  backward  from  101  thus  :  101, 98, 95,  etc. 

LESSON  XL 

1.  IN  one  pint  there  are  4  gills  ;  how  many  gills 
are  there  in  3  pints  ?     In  5  pints  ?     In  2  pints  and  3 
gills? 

2.  In  one  quart  there  are  2  pints ;  how  many  pints 
are  there  in  3  quarts  ?    In  5  quarts  ?   In  7  quarts  and 
1  pint  ? 

3.  How  many   gills   are  there  in  1   quart?    In  3 
quarts  ?    In  5  quarts  and  1  pint  ?    In  6  quarts,  1  pint, 
and  3  gills  ? 

4.  If  wine  costs  5  cents  a  gill,  what  will  one  quart 
cost  ?     What  will  one  quart  and  one  pint  cost  ?     Ono 
quart,  one  pint,  and  two  gills  ? 

5.  In  one  gallon  there  are  4  quarts  ;    how  many 
quarts  are    there   in  3  gallons?     In  5  gallons?     In  1 
gallon  nn«l  3  quarts  ? 

6.  How  many  pints   are  there  in   1   gallon  ?     In  3 
gallons  ?     In  1  gallon  and  3  quarts  ? 


42  INTELLECTUAL  [SEC.  II. 

7.  How  many  pints  are  there  in  1  gallon,  3  quarts, 
and  1  pint? 

8.  When  molasses  is  worth  7  cents  a  pint,  what  is 
1  gallon  worth  ?    What  is  1  gallon  and  1  quart  worth  ? 
1  gallon,  2  quarts,  and  1  pint  ? 

9.  How  many  gills  are  there  in  1  gallon  ? 

10.  How  many  gills  are  there  in  2  gallons  and  2 
quarts  ? 

11.  How  many  gills  are  there  in  1  gallon,  2  quarts, 
and  1  pint  ?    In  2  gallons,  1  quart,  1  pint,  and  3  gills  ? 

12.  At  2  cents  a  pint,  what  will  8  quarts  of  milk 
cost  ?     3  quarts  and  1  pint  ? 

13.  At  3  cents  a  gill,  what  will  1  pint  of  wine  cost  ? 

1  quart  ?    2  quarts  and  1  pint  ?    3  quarts,  1  pint,  and 

2  gills? 

14.  At  4  cents  a  pint,  what  will  1  gallon  of  gin  cost  ? 

15.  At  10  cents  a  quart,  what  will  1  gallon  of  mo- 
lasses cost  ?     2  gallons  and  3  quarts  ? 

1G.  At  10  cents  a  gill,  what  will  3  pints  of  brandy 
cost  ?     1  quart,  1  pint,  and  3  gills  ? 

17.  If  one  peck  of  wheat  costs  3  shillings,  how  many 
shillings  will  one  bushel  cost  ?    How  many  dollars,  if  6 
shillings  make  1  dollar  ? 

18.  If  cherries  cost  8  cents  a  quart,  what  will   1 
peck  cost  ?     What  1  peck  and  2  quarts  ? 

19.  When  beans  are  worth  5  cents  a  pint,  what  is  1 
peck  worth  ?     What  6  quarts  and  1  pint  ? 

LESSON  XII. 

1.  How  many  are  7  times  1  ?  Once    7  ? 

2.  How  many  are  7  times  2  ?  Twice  7  ? 

3.  How  many  are  7  times  3  ?  3  times  7  ? 

4.  How  many  are  7  times  4  ?  4  times  7  ? 

5.  How  many  are  7  times  5  ?  5  times  7  ? 

6.  How  many  are  7  times  0  ?  G  times  7  ? 

7.  How  many  are  7  times  7  ? 


LES.  XII.] 


ARITHMETIC. 


43 


8.  How  many  are  7  times    8  ? 

9.  How  many  are  7  times 

10.  How  many  are  7  times  10  ? 

1 1 .  How  many  are  7  times  11? 

12.  How  many  are  7  times  12  ? 

13.  How  many  are  8  times 

14.  How  many  are  8  times 

15.  How  many  are  8  times 

16.  How  many  are  8  times 

17.  How  many  are  8  times 

18.  How  many  are  8  times 

19.  How  many  are  8  times 

20.  How  many  are  8  times 

21.  How  many  are  8  times 

22.  How  many  are  8  times  10  ? 

23.  How  many  are  8  times  11  ? 

24.  How  many  are  8  times  12  ? 

25.  How  many  are  9  times 

26.  How  many  are  9  times 

27.  How  many  are  9  times 

28.  How  many  are  9  times 

29.  How  many  are  9  times 

30.  How  many  are  9  times 
81.  How  many  are  9  times 

32.  How  many  are  9  times 

33.  How  many  are  9  times 

34.  How  many  are   9  times  10  ?     10  times  9  ? 

35.  How  many  are   9  times  11  ?     11  times  9? 

36.  How  many  are  9  times  12  ?     12  times  9  ? 

37.  Count  by  4's  to  100  ;  thus,  4,  8,  12,  etc.  m 

38.  Count  backward  by  4's  ;  thus,  100,  96,  92,  etc. 

39.  Count  by  5's  to  100 ;  thus,  5,  10,  15,  etc. 

40.  Count  backward  by  5's;  thus,  100,  95,  90,  etc. 

41.  Take  7,  add  5,  multiply  by  4,  add  2,  divide  by 
5,  subtract  2,  multiply  by  4,  add  4,  divide  by  9,  divide 
by  2,  multiply  by  8,  subtract  1,  divide  by  3,  multiply 
by  4,  add  5  ;  result  ? 


8? 

8  times  7  ? 

9? 

9  times  7  ? 

0? 

10  times  7  ? 

.1? 

11  times  7? 

.2? 

12  times  7  ? 

1? 

Once    8? 

2? 

Twice  8  ? 

3? 

3  times  8  ? 

4? 

4  times  8  ? 

5? 

5  times  8  ? 

6? 

6  times  8  ? 

7? 

7  times  8  ? 

8? 

9? 

9  times  8  ? 

10? 

10  times  8  ? 

11? 

11  times  8  ? 

12? 

12  times  8  ? 

1? 

Once    9? 

2? 

Twice  9  ? 

3? 

3  times  9  ? 

4? 

4  times  9  ? 

5? 

5  times  9  ? 

6? 

6  times  9  ? 

7? 

7  times  9  ? 

8? 

8  times  9  ? 

9? 

41  INTELLECTUAL  [SEC.  II. 

LESSON  XIII. 

1.  IF  two  men  can  cut  a  certain  field  of  wheat  in 
four  days,  how  many  days  will  it  take  one  man  to  cut 
it? 

2.  If  three  men  can  do  a  piece  of  work  in  five 
days,  in  how  many  days  could  one  man  do  the  same  ? 

3.  If  a  quantity  of  provisions  will  serve  five  men 
six  days,  how  many  days  would  the  same  provisions 
serve  one  man  ? 

4.  If  a  quantity  of  provisions  will  serve  four  men 
five  days,  how  many  men   would,  the  same  provisions 
serve  one  day  ? 

5.  Six  men  built  a  piece  of  fence  in  seven  days,  but, 
the  fence  being  destroyed,  it  is  necessary  to  rebuild  it 
in  one  day  ;  how  many  men  must  be  employed  to  do 
the  work? 

6.  Paid   twenty    dollars    for   five  yards  of  cloth ; 
what  was  the  price  of  one  yard  ? 

7.  If  a  horse  can  travel  6  miles  in  one  hour,  in  how 
many  hours  can  he  travel  18  miles  ? 

8.  A  butcher  bought   sheep  at  7  dollars  a  head  ; 
how  many  did  he   buy  for  28  dollars  ?     For  42  dol- 
lars ? 

9.  At  8  dollars  a  barrel,  how  many  barrels  of  flour 
can  I  buy  for  24  dollars  ?     For  40  dollars  ? 

10.  At  7    dollars  a  barrel,  what  are  5  barrels  of 
flour  worth  ? 

11.  A  laborer   worked    5    months   for   60   dollars; 
what  did  he  receive  for  1  month  ?     For  3  months  ? 

12.  If  the  interest  of  1  dollar  is  6  cents  for  a  year, 
what  is  the  interest  of  7  dollars  for  the  same  time  ? 

13.  If  the  interest  of  1  dollar  is  6  cents  for  1  year, 
what  is  the  interest  of  the  same  sum  for  9  years  ?   For 
12  years  ? 

14.  If  a  man  can  earn  six  shillings  in  a  day,  how 
many  shillings  can  he  earn  in  5  days  ?     In  8  days  ? 


LES.  XIV.]  ARITHMETIC.  45 

15.  At  $5  a  week,  what  will  8  weeks'  board  cost  ? 

1 6.  A  man  can  earn  1 0  dollars  in  a  month  ;  how 
much  can  he  earn  in  7  months  ?     In  9  months  ? 

17.  A  man  worked   for    11  dollars  a  month,  and 
earned  77  dollars  ;  how  long  did  he  work  ? 

18.  If  72  peaches  are  divided  equally  between  8 
boys,  how  many  does  each  receive  ? 

19.  How  many  acres  of  land,  at  12  dollars  an  acre, 
may  be  bought  for  36  dollars  ?     For  60  dollars  ? 

20.  Seven  days  make  a  week ;  how  many  days  in  9 
weeks  ?     In  12  weeks  ? 

21.  A  man  can  perform  a  journey  in  63  hours  ;  in 
how  many  days,  of  9  hours  each,  can  he  perform  it  ? 

LESSON  XIV. 

1.  EIGHT  are  how  many  times  2  ?  4  ? 

2.  Ten  are  how  many  times  5?  2?  10?  1? 

3.  Twelve  are  how  many  times  2  ?    3  ?    6  ?     1  ? 

4.  Fourteen  are  how  many  times  2  ?  7  ?  1  1  ? 

5.  Fifteen  are  how  many  times  3  ?   5  ?   1  ? 
Sixteen  are  how  many  times  2  ?  4  ?  8  ? 
Eighteen  are  how  many  times  6?  9?  2  ?  3  ? 
Twenty  are  how  many  times  4?  10?   2?  5? 
Twenty-one  are  how  many  times  3  ?  7  ? 
Twenty-four  are  how  many  times  3  ?  6  ?  8  ?  2  ? 
Twenty-eight  are  how  many  times  4  ?  2  ?  7  ?  1  1  ? 
Thirty  are  how  many  times  5  ?  10  ?  6  ?  3  ?   2  ? 
Thirty-two  are  how  many  times  8?  4?  2  ?  1 G  ? 
Forty  are  how  many  times  8?  4?  5?  10? 
Forty-two  are  how  many  times  6?  7?  3?  21? 
Forty-five  are  how  many  times  3?  9?  5?  15? 
Forty-eight  are  how  many  times  4  ?  8  ?  12  ?  6  ? 
Fifty  are  how  many  times  5?  25?  10?  2? 
Fifty-four  are  how  many  times  6?3?    9?  2? 
Sixty-four   are  how  many  times  8  ?   4  ?    1 G  ? 
Seventy-two  are  how  many  times  8  ?    6  ?    9  ? 


6. 

7. 

8. 

9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 
21. 


46  INTELLECTUAL  [SEC.  II. 

22.  If  4  horses  eat  8  tons  of  hay  in  G  months,  how 
many  horses  will  eat  8  tons  in  1 2  months  ? 

23.  If  5  horses  eat  10  tons  of  hay  in  G  months,  how 
many  tons  will  7  horses  eat  in  the  same  time  ? 

24.  Bought  G  tons  of  coal  at  8  dollars  a  ton,  arid 
paid  for  it  with  cloth  at  4  dollars  a  yard ;  how  many 
yards  did  it  take  ? 

25.  If  6  men  can  do  a  piece  of  work  in  10  days*, 
how  many  men  can  do  the  same  in  15  days  ?  In  5  days  ? 

26.  If  G  men  can  do  a  piece  of  work  in  15  days,  in 
how  many  days  can  10  men  do  the  same?     30  men? 

27.  How  many  barrels  of  pork,  at  12  dollars  a  bar- 
rel, will  pay  for    10  barrels   of  flour,  at   6  dollars  a 
barrel  ? 

28.  How  many  8's  in  16  ?     In  48  ?     In  72  ? 

29.  How  many    7's  in  35  ?    63  ?    49  ?    28  ? 

30.  How  many    9's  in  36  ?   54?    27?    81? 

31.  How  many    6'sin48?    60?   72?    3G  ? 

32.  How  many  10's  in  30  ?    70?    90?  110? 

33.  How  many    5'sin50?   35?   60?    25? 

LESSON  XV. 

HEAD  across  the  page  thus :  5  and  1  are  6  ;  5  from 
G  leaves  1 ;  5  times  1  are  5  ;  5  in  5,  once  ;  etc. 


5  and    1? 

5  from    G? 

5  times     1  ? 

5  in    5  r 

5  and    2  ? 

5  from    7  ? 

5  times     2  ? 

5  in  10  ? 

5  and    3  ? 

5  from    8  ? 

5  times    3  ? 

5  in  15  r 

5  and    4  ? 

5  from    9? 

5  times     4  ? 

5  in  20  \ 

5  and    5  ? 

5  from  10  ? 

5  times    5  ? 

5  in  25  : 

5  and    6  ? 

5  from  11  ? 

5  times     6  ? 

5  in  30  : 

5  and    7  ? 

5  from  12  ? 

5  times     7  ? 

5  in  35 

5  and    8  ? 

5  from  13  ? 

5  times     8  ? 

5  in  40 

5  and    9  ? 

5  from  14? 

5  times     9  ? 

5  in  45 

5  and  10  ? 

5  from  15  ? 

5  times  10  ? 

5  in  50 

5  and  11? 

5  from  16? 

5  times  11  ? 

5  in  55 

5  and  12  ? 

5  from  17  ? 

5  times  12? 

5  in  GO 

LES.  XV.]  ARITHMETIC.  47 


6  and    1? 

6  from    7? 

6  times    1  ? 

6  in    G  ? 

6  and    2  ? 

6  from    8? 

6  times    2  ? 

6  in  12  ? 

6  and    3? 

6  from    9  ? 

6  times    3  ? 

6  in  18  ? 

6  and    4? 

6  from  10  ? 

6  times    4? 

6  in  24  ? 

6  and    5? 

6  from  11? 

6  times    5  ? 

6  in  30  ? 

6  and    6? 

6  from  12  ? 

6  times     6  ? 

6  in  36  ? 

6  and    7? 

6  from  13  ? 

6  times    7  ? 

6  in  42  ? 

6  and    8  ? 

6  from  14? 

6  times    8  ? 

6  in  48  ? 

6  and    9? 

6  from  15  ? 

6  times    9  ? 

6  in  54  ? 

6  and  10  ? 

6  from  16? 

6  times  10? 

6  in  60  ? 

6  and  11? 

6  from  17  ? 

6  times  11? 

6  in  GG  ? 

6  and  12? 

6  from  IS  ?  ( 

6  times  12? 

6  in  72  ? 

7  and    1? 

7  from    8? 

7  times    1  ? 

7  in    7? 

7  and    2? 

7  from    9  ? 

7  times    2  ? 

7  in  14? 

7  and    3? 

7  from  10? 

7  times    3  ? 

7  in  21  ? 

7  and    4? 

7  from  11? 

7  times    4  ? 

7  in  28  ? 

7  and    5  ? 

7  from  12? 

7  times    5  ? 

7  in  35  ? 

7  and    6? 

7  from  13  ? 

7  times    6  ? 

7  in  42  ? 

7  and    7? 

7  from  14? 

7  times    7  ? 

7  in  49  ? 

7  and    8? 

7  from  15  ? 

7  times    8  ? 

7  in  56? 

7  and    9? 

7  from  16? 

7  times    9  ? 

7  in  63  ? 

7  and  10  ? 

7  from  17  ? 

7  times  10  ? 

7  in  70  ? 

7  and  11? 

7  from  18? 

7  times  11? 

7  in  77  ? 

7  and  12? 

7  from  19? 

7  times  12  ? 

7  in  84? 

Sand    1? 

8  from    9  ? 

8  times    1  ? 

Sin    8? 

8  and    2  ? 

8  from  10? 

8  times    2  ? 

8  in  16? 

Sand    3? 

8  from  11? 

8  times    3  ? 

Sin  24? 

Sand    4? 

8  from  12? 

8  times    4? 

8  in  32  ? 

8  and    5  ? 

8  from  13  ? 

8  times    5  ? 

8  in  40  ? 

8  and    6  ? 

8  from  14? 

8  times    6? 

8  in  48  ? 

Sand    7? 

8  from  15? 

8  times    7  ? 

8  in  56? 

Sand    8? 

8  from  16? 

8  times    8? 

8  in  64  ? 

Sand    9? 

8  from  17? 

8  times    9  ? 

S  in  72  ? 

Sand  10? 

8  from  18  ? 

8  times  10  ? 

8  in  80  ? 

S  and  1  1  ? 

8  from  ID? 

8  times  11? 

8  in  88  ? 

8  and  12? 

8  from  20  ? 

8  times  12  f 

Sin  96? 

48  INTELLECTUAL  [SEC.  Ill 

SECTION  THIRD. 

LESSON  I. 

REMARK.  When  any  thing  is  divided  into  two  equal 
parts,  one  of  the  parts  is  called  one  half  of  the  thing ; 
so  when  any  number  is  divided  into  two  equal  parts, 
one  of  these  parts  is  called  one  half  of  the  number. 

1.  If  an  apple  is  worth  two  cents,  what  is  one  half 
of  it  worth  ? 

Ans.  It  is  worth  one  half  of  two  cents. 

2.  What  is  one  half  of  two  cents  ? 
Ans.  One  half  of  two  cents  is  one  cent. 

3.  Why  ?     Ans.  Because,  if  we  divide  two  cents 
into  two  equal  parts,  one  of  the  parts  is  one  cent. 

4.  How  many  halves  of  an  apple  make  a  whole 
apple  ? 

5.  How  many  halves  of  a  pear  make  a  whole  pear  ? 

6.  Are  two  halves  of  a  dollar  equal  to  a  whole 
dollar  ? 

Ans.  Yes.  Two  halves  of  any  thing  make  the  whole 
of  that  thing. 

7.  If  you  can  buy  a  pear  for  two  cents,  what  part 
of  it  can  you  buy  for  one  cent  ? 

8.  One  is  what  part  of  two  ? 
Ans.  One  is  one  half  of  two. 

9.  If  you  can  buy  one  pear  for  two  cents,  how  many 
pears  can  you  buy  for  three  cents  ? 

10.  Three  are  how  many  times  two  ? 
Ans.  Once  two  and  one  half  of  two. 

11.  If  you  can  buy  one  yard  of  cloth  for  two  dollars, 
how  many  yards  can  you  buy  for  four  dollars  ? 

12.  Four  are  how  many  times  two  ? 

13.  Two  is  what  part  of  four  ? 

14.  Six  are  how  many  times  two? 

15.  Five  are  how  many  times  two  ? 
Ans.  Two  times  two  and  one  half  of  two. 


LES.  I.]  ARITHMETIC.  49 

16.  If  two  dollars  will  buy  one  barrel  of  apples,  how 
many  barrels  will  five  dollars  buy  ? 

17.  If  two  dollars  will  buy  a  bushel  of  wheat,  how 
many  bushels  will  seven  dollars  buy  ? 

18.  Eight  are  how  many  times  two  ? 

19.  Nine  are  how  many  times  two  ? 

20.  Ten  are  how  many  times  two  ? 

REMARK.  When  any  thing  or  any  number  is  divided 
into  three  equal  parts,  one  of  these  parts  is  called  one 
third  of  the  thing  or  one  third  of  the  number  ;  two  of 
the  parts  are  two  thirds  of  the  thing  or  of  the  number. 

21.  How  many  thirds  of  an  apple  make  a  whole 
apple  ? 

22.  If  a  load  of  wood  is  worth  three  dollars,  and  if 
it  is  divided  into  three  equal  parts,  what  will  one  of 
the  parts  be  worth ;  that  is,  what  will  one  third  of  the 
load  be  worth  ? 

23.  What  is  one  third  of  three  dollars  ? 

24.  Suppose  the  load  to  be  divided  as  before,  what 
will  two  of  the  parts  be  worth  ;   that  is,   what   will 
two  thirds  of  the  load  be  worth  ? 

25.  What  is  two  thirds  of  three  ? 

26.  If  a  barrel  of  apples  is  worth  three  dollars,  what 
part  of  a  barrel  will  one  dollar  buy  ?     What  part  of  a 
barrel  will  two  dollars  buy  ? 

27.  One  is  what  part  of  three  ? 
Ans.  One  is  one  third  of  three. 

28.  Two  is  what  part  of  three  ? 

Ans.  Two  is  two  times  one  third  of  three ;  that  is, 
two  is  two  thirds  of  three. 

29.  If  you  can  buy  a  pound  of  tea  for  three  shillings, 
how  much   can   you   buy  for  four    shillings  ?     How 
much  for  five  shillings  ?     For  six  shillings  ? 

30.  Four  are  how  many  times  three  ? 
Ans.  Once  three  and  one  third  of  three. 

31.  Five  are  how  many  times  three? 

32.  Six  are  how  many  times  three  ? 

4 


50  INTELLECTUAL  [SEC.  III. 

83.  If  apples  are  worth  three  dollars  a  barrel,  how 
many  barrels  can  you  buy  for  seven  dollars  ?  How 
many  for  eight  dollars  ? 

34.  What  is  meant  by  one  third  of  any  thing  ? 
Am.  One  third  of  any  thing  is  one  of  the  three  equal 

parts  into  which  that  thing  is  divided.     See  Remark 
after  Example  20. 

35.  What  is  meant  by  two  thirds  of  any  thing  ? 

36.  Nine  are  how  many  times  three  ? 

37.  Ten  are  how  many  times  three  ? 

LESSON  IL 

1.  WHAT  is  meant  by  one  fourth  of  a  thing? 

Ans.  One  of  the  four  equal  parts  into  which  the  thing 
is  divided. 

2.  What  is  meant  by  two  fourths,  or  three  fourths, 
of  any  thing  or  of  any  number  ? 

3.  If  a  cake  is  worth   4  cents,  and  it  is  cut  into  4 
equal  parts,  what  is   1  of  the  parts  worth ;  that  is, 
what  is  1  fourth  of  the  cake  worth?     What   are  2 
fourths  of  it  worth  ?     What  are  3  fourths  of  it  worth  ? 

4.  If  you  can  buy  a  cord  of  wood  for  4  dollars,  what 
part  of  a  cord  can  you  buy  for  1  dollar  ?     What  part 
for  2  dollars  ?     For  3  dollars  ? 

5.  What  part  of  four  is  one  ? 
Ans.  One  is  one  fourth  of  four. 

6.  What  part  of  four  is  two  ? 

Ans.   Two  fourths,  or  one  half,  of  four. 

7.  What  part  of  four  is  three  ? 
.4 /is.   Three  fourths  of  four. 

8.  How  many  fourths  make  a  whole  one  ? 

9.  If  you  can  buy  a  yard  of  cloth  for  four  dollars, 
how  much  can  you  buy  for  5  dollars  ?     How  much  for 
6  dollars?     For  7  dollars? 

10.  Five  are  how  many  times  four  ? 
Ans.  Once  4  and  one  fourth  of  4. 


LES.  II.]  ARITHMETIC.  Si- 

ll. Six  are  how  many  times  4? 
Am.  Once  4  and  two  fourths  of  4 ;  or,  once  4  and 

one  half  of  4. 

12.  Seven  are  how  many  times  4  ? 
Ans.  Once  4  and  three  fourths  of  4. 

13.  Eight  are  how  many  times  4  ? 

14.  If  4  barrels  of  apples  will  buy  1  ton  of  coal,  how 
many  tons  will  9  barrels  buy  ?     How  many  tons  will 
10  barrels  buy  ?     How  many  tons  will  11  barrels  buy  ? 

15.  Twelve  are  how  many  times  4  ? 

16.  Thirteen  are  how  many  times  4  ? 

17.  Fourteen  are  how  many  times  4  ? 

18.  Fifteen  are  how  many  times  4Y 

19.  Sixteen  are  how  many  times  4  ? 

20.  What  is  one  fourth  of  4  ? 
Ans.  One  fourth  of  4  is  1. 

21.  Why?     Ans.  Because,  if  we  divide  4  into  four 
equal  parts,  one  of  the  parts  is  1. 

22.  What  is  two  fourths,  or  one  half,  of  4. 

23.  What  is  three  fourths  of  4  ? 

24.  If  one  half  of  an  apple  costs  1  cent,  what  will 
the  whole  apple  cost  ? 

Solution.  Since  one  half  of  the  apple  costs  1  cent, 
two  halves,  or  the  whole  apple,  will  cost  two  times  1 
cent,  which  are  2  cents. 

25.  If  one  half  of  a  barrel  of  flour  is  worth  4  dollars, 
what  is  a  whole  barrel  worth  ?     Why  ? 

26.  If  one  third  of  a  melon  is  worth  4  cents,  what 
are  two  thirds  of  it  worth  ?     What  is  the  whole  melon 
worth  ? 

27.  If  one  fourth  of  a  pie  costs  5  cents,  what  will 
two  fourths,  or  one  half,  of  the  pie  cost  ?     What  will 
three  fourths  of  it  cost  ?     What  the  whole  pie  ? 

28.  What  is  one  half  of  6  apples  ? 
Ans.  Three  apples. 

29.  Why  ?     Ans.  Because,  if  6  apples  are  divided 
into  two  equal  parts,  each  part  is  3  apples. 


52  INTELLECTUAL  ^  [SEC.  III. 

30.  What  is  one  half  of  8  cents  ?     Why  ? 

31.  What  is  one  half  of  12  oranges  ?     Why  ? 

32.  What  is  one  half  of  10  ?     Why  ? 

33.  What  is  one  third  of  6  apples  ? 
Ans.  Two  apples. 

34.  Why  ?     Ans.  Because,  if  6  apples  are  divided 
into  three  equal  parts,  each  part  is  2  apples. 

35.  What  is  one  third  of  12  lemons  ?     Why  ? 

36.  What  is  two  thirds  of  12  lemons  ?     Why  ? 

37.  What  is  one  third  of  15  dollars  ?     What  is  two 
thirds  of  15  dollars  ? 

38.  What  is  one  third  of  21  ?     Two  thirds  of  21  ? 

39.  What  is  one  half  of  3  apples  ? 

Ans.  One  apple  and  one  half  of  another  apple. 

40.  What  is  one  half  of  5  apples  ? 

Ans.  Two  apples  and  one  half  of  an  apple. 

41.  What  is  one  half  of  7  apples  ? 

42.  What  is  one  half  of  9  pears  ? 

43.  What  is  one  third  of  4  oranges  ?     Two  thirds  ? 

44.  What  is  one  fourth  of  16  miles  ? 

45.  What  is  two  fourths,  or  one  half,  of  16  miles  ? 

46.  What  is  three  fourths  of  16  miles  ? 

47.  What  is  one  fifth  of  15  dollars  ? 

48.  What  is  two  fifths  of  15  dollars  ?     Three  fifths  ? 

49.  What  is  meant  by  one  fifth,  two  fifths,  etc.,  oi' 
any  number  ?     See  Remark  after  Ex.  20,  page  49. 

50.  Mary  had  two  fifths  of  a  dollar,  and  her  mother 
gave  her  another  fifth  ;  what  part  of  a  dollar  had  she 
then? 

51.  Henry  had  four  fifths  of  a  dollar,  but  he  spent 
two  fifths  of  a  dollar  for  fruit ;   what  part  of  a  dollar 
has  he  now  ? 

52.  How  many  fifths  make  a  whole  one  ? 

53.  A  boy  spent  one  fifth  of  all  his  money  on  Mon- 
day, and  two  fifths  on  Tuesday;    what   part  of  his 
money  did  he  spend  in  these  two  days  ?     What  part 
had  he  then  remaining  ? 


LES.  Ill]   rt  ARITHMETIC.  53 


LESSON  III. 

REMARK.  The  following  lines  represent  a  yard- 
stick, marked  off  or  divided  into  halves,  fourths,  and 
eighths  of  a  yard. 

One  half.  One  half. 

One  fourth.  One  fourth.  One  fourth.          One  fourth. 

1  eighth.  1  eighth.  1  eighth.  1  eighth.  1  eighth.  1  eighth.  1  eighth.  1  eighth, 

lc  One  half  equals  how  many  fourths  ?     Ans.  Two. 

2.  One  fourth  equals  how  many  eighths  ? 

3.  One  half  equals  how  many  eighths  ? 

4.  If  you  cut  an  apple  into  halves,  and   then  cut 
each  half  into  two  equal  pieces,  into  how  many  pieces 
will  the  apple  be  cut  ?     What  part  of  the  whole  apple  is 
one  of  these  small  pieces  ? 

5.  One  half  of  an  apple  is  equal  to  how  many  times 
one  fourth  of  an  apple  ? 

6.  How  many  fourths  of  an  orange  are  equal  to  one 
half  of  an  orange  ? 

REMARK.  The  following  lines  represent  a  yard- 
stick divided  into  thirds  and  sixths  of  a  yard. 

One  third.  One  third.  One  third. 

One  sixth.  One  sixth.  One  sixth.  One  sixth.  One  sixth.  One  sixth. 

7    One  third  equals  how  many  sixths  ? 

8.  If  you  cut  a  cake  into  thirds,  and  then  cut  each 
third  into  two  equal  parts,  into  how  many  equal  parts 
will  the  cake  be  cut  ?     Each  of  the  small  pieces  will 
be  what  part  of  the  whole  cake  ? 

9.  One  third  of  a  cake  is  how  many  times  one  sixth 
of  the  same  cake  ? 

10.  If  you  cut  a  pie  into  halves,  and  then  cut  each 
half  into  three  equal  parts,  what  part  of  the  pie  will 
one  of  these  small  pieces  be  ? 


5-J-  INTELLECTUAL  [SEC.  III. 

11.  One  half  of  any  thing  is  how  many  sixths  of 
the  same  thing  ? 

12.  How  many  sixths  of  an  apple  are  equal  to  one 
third  of  an  apple  ? 

13.  How  many  sixths  of  an  apple  are  equal  to  one 
half  of  an  apple  ? 

14.  If  one  half  of  an  apple  is  cut  into  four  equal 
pieces,  what  part  of  the  whole  apple  will  one  of  these 
small  pieces  be  ? 

15.  How  many  eighths  of  an  apple  make  one  half  of 
an  apple  ? 

16.  If  one  fourth  of  an  apple  is  cut  into  two  equal 
parts,  what  part  of  the  whole  apple  will  one  of  these 
small  pieces  be  ? 

17.  How  many  eighths  of  a  pear  make  one  fourth  of 
a  pear  ? 

18.  What  is  meant  by  one  eighth  of  any  thing  ? 

19.  If  a  barrel  of  flour  be  worth  8  dollars,  and  if  it 
be  divided  equally  among  8  men,  what  will  one  man's 
share  be  worth ;  that  is,  what  is  one  eighth  of  a  barrel 
worth?     What  are  two  eighths,  or  one  fourth,    of  it 
worth  ?     What  are  three  eighths  of  it  worth  ?     What 
are  four  eighths,  or  one  half,  of  it  worth  ? 

20:  If  8  dollars  will  buy  a  box  of  tea,  what  part  of  a 
box  will  1  dollar  buy  ?  What  part  will  2  dollars  buy  ? 
3  dollars?  4  dollars  ?  5  dollars  ?  6  dollars?  7  dollars? 

,21.  What  part  of  eight  is  one  ? 
•     Ans.  One  is  one  eighth  of  eight. 

22.  Two  is  what  part  of  eight  ? 

Ans.  Two  eighths,  or  one  fourth  of  eight. 

23.  Three  is  what  part  of  eight  ? 
Ans.  Three  eighths  of  eight. 

24.  Four  is  what  part  of  eight  ? 

Ans.  Four  eighths,  or  one  half  of  eight. 

25.  Five  is  what  part  of  eight  ? 

26.  Six  is  what  part  of  eight  ? 

27.  Seven  is  what  part  of  eight  ? 


* 
LES.  IV.]  ARITHMETIC.  55 

28.  Nine  are  how  many  times  eight  ? 
Ans.  Once  eight  and  one  eighth  of  eight. 

29.  Ten  are  how  many  times  eight  ? 

Ans.  Once  eight  and  two  eighths  of  eight,  or  once 
eight  and  one  fourth  of  eight. 

NOTE.  The  second  answer  to  Example  29  is  the  best,  if  the 
pupil  is  able  to  make  the  reduction.  The  teacher  should  ex- 
ercise his  own  judgment  in  all  such  questions. 

30.  Eleven  are  how  many  times  eight  ? 

31.  Twelve  are  how  many  times  eight? 

32.  Thirteen  are  how  many  times  eight  ? 

33.  Fourteen  are  how  many  times  eight  ? 

34.  Fifteen  are  how  many  times  eight  ? 

LESSON  IV. 

1 .  IF  cranberries  cost  7  cents  a  quart,  what  part  of 
a  quart  may  be  bought  for  1  cent  ?     What  part  for  2 
cents?     For  3  cents?    4  cents?   5  cents?    6  cents  ? 

2.  If  wood  is  worth  7   dollars  a  cord,  how  many 
cords  may  be  bought  for  8  dollars?     For  9  dollars? 
10  dollars  ?     12  dollars  ?     14  dollars  ? 

3.  What  is  meant  by  one   seventh,  two  sevenths, 
three  sevenths,  etc.,  of  any  thing  ? 

4.  How  many  sevenths  make  a  whole  one  ? 

5.  If  corn  is  worth  7  shillings  a  bushel,  what  is  one 
seventh  of  a  bushel  worth  ?     What  are  two  sevenths 
worth  ?     Three  sevenths  ?     Five  sevenths  ? 

6.  If  blueberries  cost  7  cents  a  quart,  what  will 
one  seventh  of  a  quart  cost  ?     Four  sevenths  ?     Six 
sevenths  ? 

7.  One  is  what  part  of  seven  ? 
Ans.  One  is  one  seventh  of  seven, 

8.  Two  is  what  part  of  seven  ? 
Ans.  Two  sevenths  of  seven. 

9.  Three  is  what  part  of  seven? 

10.  Nine  are  how  many  times  seven  ? 


56  INTELLECTUAL  [SEC.  III. 

Am.  Once  seven  and  two  sevenths  of  seven. 

11.  Ten  are  how  many  times  seven  ? 

12.  Twelve  are  how  many  times  seven  ? 

13.  Fourteen  are  how  many  times  seven  ? 

14.  Fifteen  are  how  many  times  seven  ? 

15.  When  rye  is  worth  9  shillings  a  bushel,  what  is 
one  ninth  of  a  bushel  worth  ?     What  are  two  ninths 
of  a  bushel  worth  ?     What  are  three  ninths,  or  one 
third  of  a  bushel  worth  ?     Four  ninths  ?     Five  ninths  ? 
Six  ninths,  or   two   thirds  ?     Seven   ninths  ?     Eight 
ninths  ? 

16.  When  coal  costs  7  dollars  a  ton,  what  part  of  a 
ton  can  I  buy  for  1  dollar  ?     What  part  for  2  dollars  ? 
For  3  dollars  ?     For  4  dollars  ?     For  5  dollars  ?     For 
6  dollars  ?     For  7  dollars  ?     How  much  can  I  buy  for 
8  dollars?     For  10  dollars?     For  11  dollars?    For 
12  dollars?     For  14  dollars?     For  16  dollars? 

17.  One  is  what  part  of  nine? 

18.  What  is  meant  by  one  ninth,  two  ninths,  three 
ninths,  etc.  ? 

19.  How  many  ninths  make  a  whole  one  ? 

20.  Two  is  what  part  of  nine  ? 

21.  Three  is  what  part  of  nine  ? 

22.  Four  is  what  part  of  nine? 

23.  Five  is  what  part  of  nine  ? 

24.  Six  is  what  part  of  nine  ? 

25.  Seven  is  what  part  of  nine  ? 
20,  Eight  is  what  part  of  nine  ? 

27.  Ten  are  how  many  times  nine  ? 

28.  Eleven  are  how  many  times  nine  ? 
^9.  Twelve  are  how  many  times  nine  ? 

.     30.  Fourteen  are  how  many  times  nine  ? 

31.  Fifteen  are  how  many  times  nine  ? 

32.  Seventeen  are  how  many  times  nine? 

33.  Eighteen  are  how  many  times  nine? 

34.  Twenty  are  how  many  times  nine  ? 

35.  Twenty-four  are  how  many  times  nine  ? 


LES.  V.]  AEITHMETIC.  57 

LESSON  Y. 

1.  IF  a  laborer  earns  8  shillings  in  a  half  day,  how 
much  will  he  earn  in  a  whole  day  ? 

2.  Three  is  one  half  of  what  number  ? 

Solution.  If  3  is  one  half  of  some  number,  then 
two  halves,  or  the  whole  of  the  number,  must  be  twice 
3,  which  are  6  ;  therefore  3  is  one  half  of  6  ? 

3.  Five  is  one  half  of  what  number  ?     Why  ? 

4.  If  a  boy  picks  2  quarts  of  chestnuts  in  1  hour,  how 
many  quarts  will  he  pick  in  3  hours  ? 

5.  Two  is  one  third  of  what  number  ? 

Solution.  If  2  is  one  third  of  some  number,  then 
three  thirds,  or  the  whole  of  the  number,  must  be  three 
times  2,  which  are  6 ;  therefore,  2  is  one  third  of  6. 

6.  Four  is  one  third  of  what  number  ?     Why  ? 

7.  Seven  is  one  third  of  what  number  ? 

8.  If  one  fourth  of  a  dollar  will  pay  for  6  oranges, 
how  many  oranges  may  be  bought  for  a  whole  dollar  ? 

9.  Six  is  one  fourth  of  what  number  ? 

10.  Nine  is  one  fourth  of  what  number? 

11.  Three  is  one  fifth  of  what  number  ? 

12.  Five  is  one  seventh  of  what  number  ? 

13.  Four  is  one  eighth  of  what  number  ? 

14.  If  three  fourths  of  a  pound  of  raisins  cost  15 
cents,  what  will  a  pound  cost  ? 

Solution.  If  three  fourths  cost  15  cents,  one  fourth  will 
cost  one  third  of  15  cents,  which  is  5  cents  ;  and  four 
fourths  will  cost  4  times  5  cents,  which  are  20  cents. 

15.  Charlie's  mother  said  to  him,  "  I  have  just  bought 
5  eighths  of  a  watermelon  for  15  cents ;  and  if  you  will 
tell  me  what  the  whole  melon  is  wrorth,  I  will  give  you 
money  enough  to  buy  one."     Had  ygu  been  Charlie, 
what  would  you  have  answered  ? 

1 6.  Fifteen  is  3  fourths  of  what  number  ? 

17.  Fifteen  is  5  eighths  of  what  number  ? 

18.  Twelve  is  3  fifths  of  what  number  ? 


58  INTELLECTUAL  [SEC.  III. 

19.  Twenty  is  5  sevenths  of  what  number?        ,*. 

20.  Eighteen  is  6  sevenths  of  what  number  ? 

21.  When  cherries  cost  10  cents  a  quart,  what  is  one 
tenth  of  a  quart  worth  ?     What  are  two  tenths,  or  one 
fifth,  of  a  quart  worth  ?    What  are  three  tenths  worth  ? 
What  four  tenths,  or  two  fifths  ?     What  five  tenths, 
or  one  half? 

22.  When  hay  costs  10  dollars  a  ton,  what  part  of  a 
ton   can  you   buy  for  1    dollar  ?     What  part   for   2 
dollars  ?     What  for  3  dollars  ?     For  4   dollars  ?   5 
dollars  ?    6  dollars  ?   7  dollars  ?  8  dollars  ?   How  much 
can  you  buy   for  11  dollars?     For  12   dollars?    13 
dollars  ?    15  dollars  ?    19  dollars  ?    20  dollars  ? 

23.  What  is  meant  by  one  tenth,  two  tenths,  three 
tenths,  etc.  ? 

24.  How  many  tenths  make  a  whole  one  ? 

25.  If  a  barrel  of  flour  costs  10  dollars,  what  will  one 
half  of  a  barrel  cost-  ?     What  will  1  fifth  of  a  barrel 
cost  ?   3  fifths  ?    4  fifths  ? 

26.  If  I  can  walk  4  miles  in  1  hour,  how  far  can  I 
walk  in  a  half  hour  ?     How  far  in  3  fourths  of  an 
hour  ? 

27.  If  a  man  earns  8  shillings  each  day,  in  how  many 
days    will  he   earn  25    shillings  ?   34   shillings  ?    36 
shillings  ? 

28.  If  a  man  threshes  10  bushels  of  rye  each  day,  in 
how  many  days  will  he  thresh  35  bushels  ?    44  bushels  ? 
28  bushels  ? 

29.  When  hay  is  worth  12  dollars  a  ton,  how  many 
tons  can  I  buy  for  30  dollars  ?     For  33  dollars  ? 


LESSON  VI. 

1  .  TEN  are  how 
5  ?  4  ?  3  ? 

2.  Fifteen  are  how  many  times  3  ?   5  ?   6  ? 
o.  Sixteen  are  how  many  times  4?   8?    6? 


. 

1  .  TEN  are  how  many  times  2  ?     How  many  times 
4  ?  3  ? 

5? 


LES.  VI.]  ARITHMETIC.  50 

4.  Eighteen  are  how  many  times  6?  9?  3  ?  2  ?  4  ? 

5.  Twenty  are  how  many  times  5?    10?   4?  2  ?  8? 
o.  Nineteen  are  how  many  times  6?    3?    11?    10? 

2?   5? 

7.  Twelve  are  how   many  times  4?    6?   3?   2? 
5?   8? 

8.  Seventeen  are  how  many  times  3?   5?   4?   2? 
6?   8? 

9.  Thirteen  are  how  many  times  4?   3?   5?   2?    6? 
9?   7? 

10.  Twenty-one  are  how  many  times  7?   3?    6?   8? 
2?    5?   4? 

11.  If  you  had  22  cents,  how  many  oranges  could 
you  buy,  at  4  cents  apiece  ?     How  many  at  3  cents  ? 
At  5  cents  ?     At  2  cents  ? 

12.  Twenty-two  are  how  many  times  4?    3?   5?    2? 
11?    7?    6? 

13.  Twenty-five  are  how  many  times  5  ?    2  ?    10  ? 
6?   4? 

1 4.  Twenty-three  are   how  many  times  7  ?   5  ?   4  ? 
10?    2? 

15.  Twenty-four  are  how  many  times  6  ?   8?   4?   3? 
12?   5? 

1G.  Twenty-eight  are   how  many  times  4?   8?   7? 
6?   9? 

17.  Twenty-six  are   how  many  times  2  ?    13  ?    6  ? 
4?   8? 

18.  Thirty  are  how  many  times  6  ?   10  ?   3  ?   5  ?   8  ? 
4?    7? 

19.  Twenty-seven  are  how  many  times  9?   6?   3? 
5?   7? 

20.  Twenty-nine   are   how   many  times  7  ?   3  ?   5  ? 
6?   8? 

21.  Thirty-two  are  how  many  times  8?    6?    4?   5? 
2?    16? 

22.  Thirty-one  are  how  many  times  10?    6?    4?    3? 
8?   7? 


GO  INTELLECTUAL  [SEC.  III. 

LESSON   VII. 

1.  IP  you  had  $32,  how  many  yards  of  cloth  could 
you,  buy  at  $4  a  yard?    At  $2  ?    $6?    $5?    $8?    $1? 
fto?    $7? 

2.  Thirty-three  are  how  many  times  10?    11?    6? 
4?    3?    12? 

3.  Thirty-four  are  how  many  times  6  ?    10  ?   5  ? 
8?    3?   4? 

4.  Thirty-five  are  how  many  times  7?    10?    8?    5? 
4?    6?   3? 

5.  For  36  cents,  how  many  pounds  of  sugar  can  be 
bought,  at  6  cents  a  pound  ?     At  12  cents  ?    10  cents  ? 
8  cents  ?    9  cents  ?    7  cents  ?    11  cents  ? 

6.  Thirty-six  are  how  many  times  6?    12?    10? 
8?    9?    7?    11? 

7.  Forty  are  how  many  times  8  ?    6  ?    4  ?    10  ?    9  ? 
7?   12?    11? 

8.  Forty -five  are  how  many  times  9?   8?    6?   5? 
10?    7?   3? 

9.  Forty-eight   are   how  many  times  12?    6?    4? 
8?   9? 

10.  Fifty  are  how  many  times  10?   8?   5?    4?    12? 
6  ?    7  ?    9  ? 

11.  Thirty-seven  are  how  many  times  6?    8?    10? 
12?    4?    9? 

12.  Forty-six  are  how  many  times  7  ?    8?    4?    10? 
9?    5?    11? 

13.  Forty-two  are  how  many  times  7?  10?    4?    6? 
8  ?    5  ?    9  ? 

14.  Forty-nine  are  how  many  times  7?   8?    6?    10? 
9?    4?    12? 

15.  Thirty-eight  are  how  many  times  12?    6?    4? 
9?   7?   8? 

16.  Forty-four  are  how  many  times  11?   8?    4?  9? 
6?    10? 

17.  Thirty -nine   are   how  many  times  6  ?    9  ?    12  ? 


LES.  VIII] 


AKITHMETIC. 


Gl 


18.  For  47  cents,  how  many  oranges  may  be  bought, 
at  5  cents  each  ?     At  4  cents  ?   8  cents  ?    6  cents  ?   9 
cents  ?   7  cents  ? 

19.  Forty- three  are  how  many  times  6?   8?    10? 
5?   9?   7? 

20.  Forty-one  are  how  many  times  10?    12?   4? 
6?   9?   7? 


LESSON  VIII. 


1. 

How 

many 

are 

10 

times 

1? 

Once 

10? 

2. 

How 

many 

are 

10 

times 

2? 

Twice 

10? 

3. 

How 

many 

are 

10 

times 

3? 

3 

times 

10? 

4. 

How 

many 

are 

10 

times 

4? 

4 

times 

10? 

5. 

How 

many 

are 

10 

times 

5? 

5 

times 

10? 

6. 

How 

many 

are 

10 

times 

6? 

6 

times 

10? 

7. 

How 

many 

are 

10 

times 

7? 

7 

times 

10? 

3. 

How 

many 

are 

10 

times 

8? 

8 

times 

10? 

9. 

How 

many 

are 

10 

times 

9? 

9 

times 

10? 

10. 

How 

many 

are 

10 

times 

10? 

11. 

How 

many 

are 

10 

times 

11? 

11 

times 

10? 

12. 

How 

many 

are 

10 

times 

12? 

12 

times 

10? 

13. 

How 

many 

are 

11 

times 

1? 

Once 

11? 

14. 

How 

many 

are 

11 

times 

2? 

Twice 

11  ? 

15. 

How 

many 

are 

11 

times 

3? 

3 

times 

11? 

16. 

How 

many 

are 

11 

times 

4? 

4 

times 

11? 

17. 

How 

many 

are 

11 

times 

5? 

5 

times 

11? 

18. 

How 

many 

are 

11 

times 

6? 

6 

times 

11? 

19. 

How 

many 

are 

11 

times 

7? 

7 

times 

11? 

20. 

How 

many 

are 

11 

times 

8? 

8 

times 

11? 

21. 

How 

many 

are 

11 

times 

9? 

9 

times 

11  ? 

22. 

How 

many 

are 

11 

times 

10? 

10 

times 

11? 

23. 

How 

many 

are 

11 

times 

11? 

24. 

How 

many 

are 

11 

times 

12? 

12 

times 

11? 

25. 

How 

many 

are 

12 

times 

1? 

Once 

12? 

26. 

How 

many 

are 

12 

times 

2? 

Twice 

12? 

G2  INTELLECTUAL  [SEC.  IIL 

27.  How  many  are  12  times    3  ?  3  times  12  ? 

28.  How  many  are  12  times    4?  4  times  12  ? 

29.  How  many  are  12  times    5  ?  5  times  12  ? 

30.  How  many  are  12  times    6  ?  6  times  12  ? 

31.  How  many  are  12  times    7  ?  7  times  12  ? 

32.  How  many  are  12  times    8  ?  8  times  12  ? 

33.  How  many  are  12  times    9  ?  9  times  12  ? 

34.  How  many  are  12  times  10  ?  10  times  12  ? 

35.  How  many  are  12  times  11  ?  11  times  12  ? 

36.  How  many  are  12  times  12  ? 


LESSON  IX. 

1.  Two  times  two  are  how  many  times  one  ? 

2.  Three  times  two  are  how  many  times  one  ? 

3.  Five  times  two  are  how  many  times  one  ? 

4.  Eight  times  two  are  how  many  times  one  ? 

5.  Two  times  three  are  how  many  times  one  ? 

6.  Five  times  three  are  how  many  times  one  ? 

7.  Four  times  three  are  how  many  ? 

8.  Seven  times  two  are  how  many  ? 

9.  Nine  times  three  are  how  many? 

10.  Ten  times  two  are  how  many  ? 

11.  Six  times  four  are  how  many  ? 

12.  Seven  times  three  are  how  many  ? 

13.  Ten  times  four  are  how  many  ? 

14.  Eleven  times  two  are  how  many? 

15.  Five  times  five  are  how  many  ? 

16.  Six  times  eight  are  how  many  ? 

17.  Eight  times  six  are  how  many  ? 

18.  Five  times  nine  are  how  many  ? 

19.  Four  times  eleven  are  how  many  ? 

20.  Four  times  twelve  are  how  many  ? 

21.  Six  times  twelve  are  how  many  ? 

22.  Six  times  seven  are  how  many  ? 

23.  Nine  time*  four  are  how  many  ? 

24.  Ten  times  nine  are  how  many  ? 


LES.  IX.]  ARITHMETIC.  C3 

25.  Eleven  times  six  are  how  many  ? 

26.  Eight  times  eight  are  how  many  ? 

27.  Seven  times  twelve  are  how  many  ? 

28.  Twelve  times  nine  are  how  many  ? 

29.  Twelve  times  six  are  how  many  ? 

30.  Four  times  nine  are  how  many  ? 

31.  Seven  times  eleven  are  how  many  ? 

32.  Nine  times  eight  are  how  many  ? 

33.  Ten  times  twelve  are  how  many  ? 

34.  Eight  times  three  are  how  many  ? 

35.  Six  times  nine  are  how  many  ? 

36.  Twelve  times  eight  are  how  many? 

37.  Seven  times  nine  are  how  many  ? 

38.  Seven  times  ten  are  how  many  ? 

39.  Eleven  times  eight  are  how  many  ? 

40.  Seven  times  eight  are  how  many  ? 

41.  Nine  times  nine  are  how  many? 

42.  Eleven  times  nine  are  how  many  ? 

43.  Eight  times  twelve  are  how  many  ? 

44.  Five  times  twelve  are  how  many  ? 

45.  Six  times  eleven  are  how  many  ? 

46.  Twelve  times  three  are  how  many  ? 

47.  Nine  times  five  are  how  many  ? 

48.  Eight  times  seven  are  how  many  ? 

49.  Twelve  times  seven  are  how  many  ? 

50.  Five  times  eight  are  how  many  ? 

51.  Nine  times  ten  are  how  many  ? 

52.  Nine  times  six  are  how  many  ? 

53.  Eleven  times  seven  are  how  many  ? 

54.  Three  times  nine  are  how  many  ? 

55.  Eight  times  eleven  are  how  many  ? 

56.  Twelve  times  twelve  are  how  many  ? 

57.  Eight  times  four  are  how  many  ? 

58.  Ten  times  six  are  how  many  ? 

59.  Three  times  eight  are  how  many  ? 

60.  Six  times  ten  are  how  many  ? 

61.  Eleven  times  ten  are  how  many  ? 


61  INTELLECTUAL  [SEC.  III. 

62.  Nine  times  twelve  are  how  many  ? 

63.  Five  times  eleven  are  how  many  ? 

64.  Twelve  times  ten  are  how  many  ? 

65.  Nine  times  eleven  are  how  many  ? 

66.  Nine  times  seven  are  how  many  ? 

67.  Six  times  six  are  how  many  ? 

68.  Twelve  times  four  are  how  many  ? 

69.  Ten  times  eleven  are  how  many  ? 

70.  Eleven  times  twelve  are  how  many  ? 

71.  Seven  times  six  are  how  many  ? 

72.  Eleven  times  eleven  are  how  many  ? 

73.  Eight  times  ten  are  how  many  ? 

74.  Seven  times  seven  are  how  many  ? 
•     75.  Twelve  times  five  are  how  many  ? 

76.  Ten  times  three  are  how  many? 

77.  Ten  times  seven  are  how  many  ? 

78.  Eight  times  nine  are  how  many  ? 

79.  Ten  times  ten  are  how  many  ? 

80.  Twelve  times  eleven  are  how  many  ? 

LESSON  X. 

1.  WHAT  cost  5  oranges,  at  6  cents  apiece  ? 

2.  What  cost  8  tons  of  coal,  at  7  dollars  a  ton  ? 

3.  There  is  an  orchard  consisting  of  8  rows  of  trees, 
having  1 2  trees  in  each  row  ;  how  many  trees  are  there 
in  the  orchard  ? 

4.  Twenty  shillings  make  one  pound  ;  how  many 
pence  are  there  in  a  pound  ? 

5.  How  many  gills  are  there  in  two  gallons  ? 

6.  If  one  gill  of  beer  costs  two  cents,  what  will 
one  gallon  cost  ? 

7.  Two  men  start  from  the  same  place  and  travel 
the  same  way ;  one  travels  at  the  rate  of  three  miles, 
in  an  hour,  and  the  other  seven  ;  how  far  apart  are 
they  at  the  end  of  one  hour  ?     How  far  at  the  end  of 
seven  hours  ? 


LES.  X-l  ARITHMETIC.  65 

8.  Two  men  start  from  the  same  place  and  travel 
in  opposite  directions,  one  at  the  rate  of  two  miles  in 
an  hour,  and  the  other  six ;  how  far  apart  are  they  in 
seven  hours  ?     How  far  in  ten  hours? 

9.  If  the  interest  of  one  dollar  is  six  cents  a  year, 
what  is  the  interest  of  three  dollars  for  two  years  ? 

10.  How  many  oranges,  at  4  cents  apiece,  must  be 
given  for  12  lemons,  at  3  cents  apiece  ? 

11.  How  many  pounds  of  beef,  at  9  cents  a  pound, 
will  pay  for  6  dozen  of  eggs,  at  12  cents  a  dozen? 

12.  If  8  men  can  do  a  certain  piece  of  work  in  6 
days,  in  how  many  days  can  4  men  do  the  same  ? 

13.  If  9  men  can  do  a  piece  of  work  in  8  days, 
how  many  men  can  do  the  same  in  12  days  ? 

14.  If  4  men  can  do  a  piece  of  work  in  6  days,  in 
how  many  days  can  3  men  do  twice  as  much  work  ? 

15.  A  farmer  sold  2  tons  of  hay  at  $20  a  ton,  and 
for  pay  received  8  yards  of  cloth  at  $4  a  yard,  and 
the  rest  in  money  ;  how  much  money  did  he  receive  ? 

16.  If  a  man  earns  $24  in  2  months,  what  will  2 
men  earn  in  6  months  ? 

17.  Six  times  8  are  how  many  times  12  ? 

18.  Ten  times  6  are  how  many  times  12  ?   20  ?   5  ? 

19.  Eight  times  8  are  how  many  times  4?   32? 
16? 

20.  Seven  times  10  are  how  many  times  5  ?  7  ? 
14? 

21.  Seventy-two  are  how  many  times  8  ?   6  ?   9  ? 
12?   4? 

22.  Eighty  are  how  many  times  4  ?   8  ?    20  ?    10  ? 
5?   16? 

23.  Seventy-five  are    how  many  times   25  ?   5  ? 
15?   3? 

24.  Eighty-four  are  how  many  times  12  ?    6  ?   7  ? 
21?   4? 

25.  Ninety-six  are  how  many  times  8?    16?   12? 
24  ?   48  ?   32  ? 


66  INTELLECTUAL  [SEC.  III. 

26.  One  hundred  are  how  many  times  10  ?   20  ? 
25?   50?   2?   4?   5? 

27.  One  hundred  and  eight  are  how  many  times  1 2  ? 
9  ?   54  ?   4  ?   27  ? 

28.  One  hundred  and  twenty  are  how  many  times 
12?   20?   10?   40? 

29.  One  hundred  and  twenty-five  are  how  many 
times  25?   5?    125?   1? 

30.  One  hundred   and   thirty-two  are   how  many 
times  11  ?   22?   44?    12?    6? 

31.  One   hundred   and  forty-four   are   how   many 
times  12  ?   24  ?   48  ?   6  ? 

LESSON  XI. 
READ  rapidly  and  accurately  across  the  page. 


9 

and 

1? 

9 

from 

10? 

9 

times 

1? 

9 

in 

9? 

9 

and 

2? 

9 

from 

11? 

9 

times 

2? 

9 

in 

18? 

9 

and 

3? 

9 

from 

12? 

9 

times 

3? 

9 

in 

27? 

9 

and 

4? 

9 

from 

13? 

9 

times 

4? 

9 

in 

36? 

9 

and 

5? 

9 

from 

14? 

9 

times 

5? 

9 

in 

45? 

9 

and 

6? 

9 

from 

15? 

9 

times 

6? 

9 

in 

54  ? 

9 

and 

7? 

9 

from 

16? 

9 

times 

7? 

9 

in 

63? 

9 

and 

8? 

9 

from 

17? 

9 

times 

8? 

9 

in 

72? 

9 

and 

9? 

9 

from 

18? 

9 

times 

9? 

9 

in 

81  ? 

9 

and 

10? 

9 

from 

19? 

9 

times 

10? 

9 

in 

90  ? 

0 

and 

11? 

9 

from 

20? 

9 

times 

11? 

9 

in 

1)9  ? 

9 

and 

12? 

9 

from 

21? 

9 

times 

12? 

9 

in 

108? 

10 

and 

1? 

10 

from 

11? 

10 

times 

1? 

10 

in 

10? 

10 

and 

2? 

10 

from 

12? 

10 

times 

2? 

10 

in 

20? 

10 

and 

3? 

10 

from 

13? 

10 

times 

3? 

10 

in 

30? 

10 

and 

4? 

10 

from 

14? 

10 

times 

4? 

10 

in 

40? 

10 

and 

5? 

10 

from 

15? 

10 

times 

5? 

10 

in 

50? 

10 

and 

6? 

10 

from 

16? 

10 

times 

6? 

10 

in 

60? 

10 

and 

7? 

10 

from 

17? 

10 

times 

7? 

10 

in 

70? 

10 

and 

8? 

10 

from 

18? 

10 

times 

8? 

10 

in 

80? 

10 

and 

9? 

10 

from 

19? 

10 

times 

9? 

10 

in 

90? 

LES.  XII.]  ARITHMETIC.  67 


10 

and 

10? 

10 

from 

20? 

10 

times 

10? 

10 

in 

100? 

10 

and 

11? 

10 

from 

21? 

10 

times 

11? 

10 

in 

110? 

10 

and 

12? 

10 

from 

22? 

10 

times 

12? 

10 

in 

120? 

11 

and 

1? 

11 

from 

12? 

11 

times 

1? 

11 

in 

11? 

11 

and 

2? 

11 

from 

13? 

11 

times 

2? 

11 

in 

22  ? 

11 

and 

3? 

11 

from 

14? 

11 

times 

3? 

11 

in 

33? 

11 

and 

4? 

11 

from 

15? 

11 

times 

4? 

11 

in 

44? 

11 

and 

5? 

11 

from 

16? 

11 

times 

5? 

11 

in 

55  ? 

11 

and 

6? 

11 

from 

17? 

11 

times 

6? 

11 

in 

60? 

11 

and 

7? 

11 

from 

18? 

11 

times 

7? 

11 

in 

77? 

11 

and 

8? 

11 

from 

19? 

11 

times 

8? 

11 

in 

88? 

11 

and 

9? 

11 

from 

20? 

11 

times 

9? 

11 

in 

99? 

11 

and 

10? 

11 

from 

21? 

11 

times 

10? 

11 

in 

110? 

11 

and 

11? 

11 

from 

22? 

11 

times 

11? 

11 

in 

121? 

11 

and 

12? 

11 

from 

23? 

11 

times 

12? 

11 

in 

132? 

12 

and 

1? 

12 

from 

13? 

12 

times 

1? 

12 

in 

12? 

12 

and 

2? 

12 

from 

14? 

12 

times 

2? 

12 

in 

24? 

12 

and 

3? 

12 

from 

15? 

12 

times 

3? 

12 

in 

3(>  ? 

12 

and 

4? 

12 

from 

16? 

12 

times 

4? 

12 

in 

48? 

12 

and 

5? 

12 

from 

17? 

12 

times 

5? 

12 

in 

60? 

12 

and 

6? 

12 

from 

18? 

12 

times 

6? 

12 

in 

72? 

12 

and 

7? 

12 

from 

19? 

12 

times 

7? 

12 

in 

84? 

12 

and 

8? 

12 

from 

20? 

12 

times 

8? 

12 

in 

90? 

12 

and 

9? 

12 

from 

21? 

12 

times 

9? 

12 

in 

108? 

12 

and 

10? 

12 

from 

22? 

12 

times 

10? 

12 

in 

120  ? 

12 

and 

11? 

12 

from 

23? 

12 

times 

11? 

12 

in 

132? 

12 

and 

12? 

12 

from 

24? 

12 

times 

12? 

12 

in 

144? 

LESSON  XII. 

1.  FIFTY-ONE  are  how  many  times   10?    5?   3? 
6?   9?   7?  8? 

2.  Fifty-four  are  how  many  times  9?    10?    6?   7? 
8  ?    12?    11? 

3.  Fifty-two   are   how  many   times    4  ?    8  ?    12  ? 
13?    10?   7?    6? 

4.  Sixty  are  how  many  times  6  ?    10?   8?    7?  12? 


C8  INTELLECTUAL.  [SEC.  III. 

r>.  Fifty-six  are  how  many  times   7?   8?    9?    11? 
12?    6?   5? 

6.  Fifty-three  are  how  many  times  7  ?    10  ?    9  ? 
12?   4?    6? 

7.  Fifty-five  are  how  many  times    11?    10?   5? 
6?,  9?   8? 

8.  Fifty-eight  are  how  many  times  9  ?    6  ?    10  ? 
8?   7?   5? 

9.  Fifty-seven  are  how  many  times  12?    11?   5? 
10?   8?   6? 

10.  Fifty-nine  are  how  many  times  10?   5?   12? 
8?   7?   9? 

11.  Sixty-four  are  how   many  times  8?   9?    10? 
12?    6?   5? 

12.  Sixty-five  are  how  many  times   10  ?   5  ?    12  ? 
9?   7?   8? 

13.  Sixty-two  are  how  many  times  12?    10?    9? 
7?   8?   5? 

14.  Sixty-three  are  how  many  times   9  ?   7  ?   8  ? 
5?    12?   6? 

15.  Sixty-one  are  how  many  times   12?    10?   8? 
5?    6?   9? 

16.  Sixty-six  are   how  many  times   6?    11?    10? 
9?.  12?   8? 

17.  Sixty-nine   are   how   many  times  6?   12?  9? 
8?   7?    11? 

18.  Sixty-seven  are  how  many  times  8?   7?    11? 
12?  5?   9? 

19.  Sixty-eight  are  how  many  times  11?    12?   8? 
7?    10?   6? 

20.  Seventy  are  how  many  times  10  ?   7  ?   12  ?   5  ? 

21.  Seventy-five  are  how  many  times  10?   5?   12? 
6?   7?   9? 

22.  Doctor  May  has  72  miles  to  ride ;  how  many 
hours  will  it  take  him,  if  he  rides  at  the  rate  of  0 
miles  an  hour  ?     At  the  rate  of  8  miles  ?    10  miles  ? 
12  miles?    6  miles  ?   5  miles?   7  miles  ?    11  miles? 


LES.  XII.]  ARITHMETIC.  69 

23.  Seventy-two  are  how  many  times  9  ?   8  ?    10  ? 
12?    6? 

24.  Seventy-six  are  how  many  times  12  ?    10  ?    6? 
11?   5? 

25.  Seventy-eight  are  how  many  times  11  ?   7  ?   8  ? 
10?   9? 

26.  Seventy-four  are  how  many  times  9  ?   10  ?   8  ? 
7?   12? 

27.  Seventy-seven  are  how  many  times  11  ?   7  ?   9  ? 
8?   10? 

28.  Seventy-nine  are  how  many  times  11?   7?   8? 
10?    9? 

29.  Seventy-one  are  how  many  times  10  ?   8  ?   7  ? 
9?    6? 

30.  Seventy- three  are  how  many  times  7  ?   9  ?    10  ? 
6?    12? 

31.  Eighty-four  are  how  many  times  7?    12?    10? 
9?   11? 

32.  Ninety-six   are  how  many  times    12  ?   8  ?   9  ? 
10?    6? 

33.  If  you  had  $80,  how  many  tons  of  hay  could  you 
buy  at  $10  a  ton?     How  many  at  $12  ?     At  $8?     At 
If?  At.  $6?   At  $9?  At  $11? 

34  Eighty  are  how  many  times  10  ?    12  ?   8  ?   7  ? 
6?   9?    11  ? 

35.  Ninety-two  are  how  many  times  10  ?   8  ?   9  ? 
7?    12?    6? 

36.  Ninety-five  are  how  many  times  9  ?    10  ?    6  ? 
8?   7?    11? 

37.  Eighty-one  are  how  many  times  8  ?    12  ?    10  ? 
9?   7?    6? 

38.  Eighty-five  are  how  many  times  7  ?    10  ?   8  ? 
12?   9?    11? 

39.  Ninety-one  are  how  many  times  9  ?   8  ?    10  ? 
12?   7?    11? 

40.  Ninety,  are  how  many  times  10  ?    12  ?   7  ?   9  ? 
8?    6? 


70  INTELLECTUAL  [Sso.  III. 

41.  Ninety-eight  are  how  many  times  9  ?   8  ?    12  ? 
7?    10?    11? 

42.  Eighty-two  are  how  many  times  8  ?    9  ?  10  ? 
12?   11?    7? 

43.  One  hundred  are  how  many  times  10?   9?    12? 
11?   8? 

44.  Eighty-seven  are  how  many  times  7?    11?   12? 
10?   8?   9? 

45.  Eighty-three  are  how  many  times  9  ?   8  ?   10  ? 
12?   7?   11? 

46.  Eighty-nine  are  how  many  times  10?   8?   11  ? 
12?   7?   9? 

47.  Ninety-nine  are  how  many  times  9?    11?   12? 
8?   7?    10? 

48.  Ninety-four  are  how  many  times  12  ?   7  ?   10  ? 
9?   8?   11? 

49.  Eighty-six  are  how  many  times   7?    10?   8? 
9?    11?    12? 

50.  Ninety-seven  are  how  many  times  10?   9?   12? 
8?    11? 

51.  Eighty-eight  are  how  many  times  10?   8?   12? 
11?   7?   9? 

LESSON  XIII. 

1.  A  FARMER  has  30  hens  in  one  yard,  and  50  in 
another ;  how  many  hens  has  he  in  both  yards  ? 

Solution.  30  is  3  tens,  and  50  is  5  tens ;  3  tens  and 
5  tens  are  8  tens,  or  80 ;  therefore,  the  farmer  has  80 
hens  in  the  two  yards. 

2.  How  many  are 

3  and  2  ?          30  and  20  ?          300  and  200  ? 

3.  4  and  3  ?          40  and  30  ?          400  and  300  ? 

4.  8  and  5  ?          80  and  50  ?          800  and  500  ? 

5.  7  _[_  4  ?          70  -f  40  ?          700  +  400  ? 

6.  7  -j-  7  ?          70  -f-  70  ?          700  +  700  ? 

7.  John  bought  a  knife  for  45  cents,  and  a  top  for 
23  cents  ;  what  did  he  pay  for  both  ? 


LES.  XIII.]  ARITHMETIC.  71 

Solution.     40  and  20  are  60,  and  5  and  3  are  8 ; 
60  and  8  are  68  ;  therefore,  he  paid  68  cents  for  both. 

8.  How  many  are  48  and  35  ? 

Solution.     40  and  30  are  70,  and  8  and  5  are  13  ; 
70  and  13  are  83  ;  therefore,  48  and  35  are  83. 

9.  How  many  are 

2  and  3  ?  12  and  13  ?  42  and  53  ? 

10.  5  and  4  ?  25  and  34  ?  65  and  24  ? 

11.  5  +  3  ?  25  -4-  43  ?  55  +  73  ? 
•      12.  8  +  4  ?  28  -f  34  ?  68  -f  74  ? 

13.  A  farmer  having  50  cows,  sold  20  of  them  ; 
how  many  had  he  remaining  ? 

14.  How  many  are 

5  less  2  ?  50  less  20  ?  500  less  200  ? 

15.  7  less  3  ?  70  less  30  ?  700  less  300  ? 

16.  6  —  2  ?  60  —  20?  600  —  200? 

17.  9  —  5?  90  —  50?  900  —  500? 

18.  A  farmer  having  $75,  paid  $32  for  a  colt ;  how 
many  dollars  had  he  left  ? 

Solution.  $75  are  $70  and  $5  ;  $32  are  $30  and 
$2  ;  $70  less  $30  are  $40,  and  $5  less  $2  are  $3,  and 
$40  and  $3  are  $43  ;  therefore,  he  had  $43  left. 

19.  A  man  having  $53,  paid  $18  for  a  coat;  how 
many  dollars  had  he  left  ? 

Solution.  $53  are  $40  and  $13  ;  $18  are  $10  and 
$8  ;  $40  less  $10  are  $30,  and  $13  less  $8  are  $5  ; 
$30  and  $5  are  $35  ;  therefore,  etc. 

20.  How  many  are 

5  less  3  ?  65  less  23  ?  95  less  43  ? 

21.  8  less  3  ?  38  less  13  ?  78  less  53  ? 

22.  6  —  4  ?  56  —  24  ?  96  —  44  ? 

23.  15  —  7  ?  65  —  27  ?  52  —  37  ? 

24.  At   $40  per  acre,  what  will  2  acres  of  land 
cost  ? 

25.  How  many  are 

2  times  4  ?          2  times  40  ?          2  times  400  ? 

26.  3  limes  2  ?          3  times  20  ?          3  times  200  ? 

27.  3    X     3  ?         30     X      3  ?      300     X        3  ? 


72  INTELLECTUAL  [SEC.  III. 

28.  At  $23  per  acre,  what  will  6  acres   of  land 
cost? 

Solution.  6  times  $20  are  $120,  and  6  times  $3  are 
$18  ;  §120  and  $18  are  $138  ;  therefore,  etc. 

29.  How  many  are 

5  times  3  ?  5  times  23  ?  5  times  03  ? 

30.  6  times  2  ?  G  times  42  ?  6  times  G2  ? 

31.  8    X      2  ?        38    X       2  ?         68     x      2  ? 

32.  7    X      3  ?         37     X       3  ?         57     X      8  ? 

33.  I  have  3  equal  fields  which  together  contain  73 
acres ;  how  many  acres  are  there  in  each  field  ? 

Solution.  73  equals  60  and  13  ;  £  of  60  is  20,  and 
J  of  13  is  4J ;  20  and  4J  are  24-J  ;  therefore,  etc. 

34.  What  is  J-  of    6  ?    '        Of  60  ?  Of  600  ? 

35.  What  is  J  of    8  ?  Of  28  ?  Of    58  ? 

36.  What  is  |  of    8  ?  Of  38  ?  Of    98  ? 

37.  How  many  are  8  -f-  4  ?      28  -f-  4  ?      88  -5-  4  ? 

38.  How  many  are  9  ~  4  ?      49  -~  4  ?      69  -f-  4  ? 

39.  How  many  times 

3  in     6  ?  3  in  60  ?  3  in  600  ? 

40.  4  in    8  ?  4  in  80  ?  4  in  800  ? 

41.  5  in    8  ?  5  in  38  ?  5  in    78  ? 


LESSON  XIV. 

1.  FOR  50  cents,  how  many  dozen  of  eggs  can  be 
bought,  at  25  cents  a  dozen  ?     At  12  cents  a  dozen? 

2.  If  you  have  56  cents,  how  many  pounds  of  sugar 
can  you  buy,  at  7  cents  a  pound  ?     At  8  cents  ?     At 
10  cents  ? 

3.  Two  trains  of  cars,  64  miles  apart,  are  running 
the  same  way  ;  in  how  many  hours  will  they  be -to- 
gether, if  the  hindmost  train  gains  upon  the  other  8 
miles  an  hour?     In   how   many  hours   if  it  gains   4 
miles  an  hour  ?     If  6  miles  ? 

4.  How  many  tons  of  hay,  at  $12  a  ton,  can  I  buy 
for  $72  ?     How  many  at  $10  a  ton  ?     At  $15  ? 

5.  How  many  dresses,  containing    12  yards  each, 


LES.  XIV.]  ARITHMETIC.  73 

can  be  made  from  48  yards  of  silk  ?     How  many 
containing  1 6  yards,  each  ? 

6.  How  many  cords  of  wood,  at  $7  a  cord,  can  be 
bought  for  $84  ?     How  many  cords,  at  $8  a  cord  ? 

7.  If  there  are  12  months  in  a  year,  how  many 
years  are  there  in  96  months  ?     In  75  months  ? 

8.  If  there  are   30  days  in  a  month,  how  many 
months  are  there  in  90  days  ?    In  60  days  ? 

9.  If  there  are  16  ounces  in  a  pound,  how  many 
pounds  are  there  in  80  ounces  ?     How  many  if  there 
are  12  ounces  in  a  pound  ? 

10.  How  many  pounds   of  raisins,  at  11  cents  a 
pound,  can  you  buy  for  55  cents  ?     How  many  at  10 
cents  a  pound?     At  15  cents  ? 

1 1.  Six  men  bought  a  houselot  for  $96 ;  their  shares 
being  equal,  what  did  each  man  pay  ? 

12.  Hired  a  horse  and  carriage  for  77  cents,  and 
rode  7  miles ;  what  was  the  price  per  mile  ? 

13.  A  man  vhired  a  horse  and  carriage  for  a  ride, 
agreeing  to  pay  12  cents  a  mile;  he  paid  87  cents; 
how  far  did  he  ride  ? 

14.  Bought  15  cords  of  wood  for  $75;  what  was 
the  price  per  cord  ? 

15.  Mr.  Holt  can  do  a  piece  of  work  in  78  hours  ; 
how  many  days  will  it  take  him  to  do  it,  if  he  works 
12  hours  each  day  ?     How  many  if  he  works  10  hours 
each  day  ? 

16.  One  man  can  do  a  piece  of  work  in  90  hours; 
in  how  many  hours  can  6  men  do  it?    10  men?   12 
men  ? 

17.  One  man  can  do  a  piece  of  work  in  90  hours ; 
in  how  many  hours  can  6  men  do  half  as  much  work  ? 
In  how  many  hours  can  10  men  do  twice  as  much 
work  ? 

18.  A  dairy  woman  wishes  to  put  75  pounds   of 
butter  into  5  boxes ;  how  many  pounds  shall  she  put 
into  each  box  ? 


74  INTELLECTUAL  [SEC.  Ill 

19.  Eight  cheeses  weigh  100  pounds ;  what  is  their 
average  weight? 

20.  If  an   orange   is  worth   6   apples,  how  many 
oranges  are  66  apples  worth  ? 

21.  If  there  are  20  shillings  in  1  pound,  how  many 
pounds  are  there  in  80  shillings  ?     In  85  shillings  ? 

'2'2.  How  many  miles  in  96  furlongs,  if  there  are  8 
furlongs  in  1  mile  ?  How  many  miles  in  82  furlongs  ? 
In  78  furlongs  ? 

23.  At  12  cents  a  pound,  how  many  pounds  of  beef 
can  be  bought  for  144  cents  ?     For  93  cents? 

24.  How  many  wheelbarrows,  at  7  dollars  apiece, 
can  be  bought  for  84  dollars  ?     For  63  dollars  ? 

25.  A  boy  sold   6  doves  for  75  cents ;  how  many 
cents  did  he  receive  for  1  dove  ?     For  3  doves  ?     For 
4  doves  ? 

26.  A  boy  sold  chickens  at  25  cents  apiece,  and 
received  1  dollar,  or  100  cents,  for  them ;  how  many 
chickens  did  he  sell  ? 

27.  If  wine  is  worth  20  cents  a  pint,  how  many 
pints  may  be  bought  for  1  dollar  ?     How  many  quarts  ? 

28.  If  brandy  is  worth  20  cents  a  gill,  how  many 
gills  may  be  bought  for  1  dollar  ?     How  many  pints  ? 

29.  What  is  the  price  of  a  shawl,  if  9  shawls  cost 
$108? 

30.  A  boy  divided  80  chestnuts  equally  among  5  of 
his  companions ;  how  many  did  he  give  to  each  ? 

31.  If  8  bushels  of  apples  make  1  barrel  of  cider, 
how  many  barrels  will  92  bushels  make  ?   74  bushels  ? 
78  bushels  ? 

32.  At  $10  a  barrel,  how  many  barrels  of  flour  can 
be  bought  for  $85  ?     For  $92  ? 

33.  Eight  times  10  are  how  many  times  8  ? 

34.  Eight  times  11  are  how  many  times  12  ? 

35.  A  man  divided  $84  equally  among  his  3  sons 
and  4  daughters ;  how  many  dollars  did  he  give  to 
each? 


LES.  I.]  ARITHMETIC.  75 

36.  A  boy  having  7  melons,  gave  away  2  of  them, 
and  sold  the  rest  for  $1 ;  what  did  he  receive  for  each 
of  those  he  sold  ? 

37.  A  man  having    75  dollars,  bought  7  sheep,  and 
had  $5  left ;  what  did  he  pay  for  each  sheep  ? 

38.  A  boy  bought  5  hens  at  20  cents  each,  arid 
paid  for  them  with  apples  at  10  cents  a  dozen ;  how 
many  dozen  did  it  take  ? 

39.  A  man  had  75  sheep,  and  bought  5  more  ;  he 
then  divided   them   equally  in    8    pens;  how  many 
sheep  did  he  put  in  each  pen  ? 

40.  A  boy  had  50  peaches,  and  found  22  more  ;  he 
then  divided  all  of  them  equally  among  himself  and 
1 1  of  his  companions  ;  how  many  did  he  give  to  each  ? 


SECTION  FOURTH. 
LESSON  I. 

REMARKS.  1.  A  single  thing  of  any  kind  is  called  a 
unit  or  one.     A  unit  is  represented  by  the  figure  10 

2.  When  any  thing   is  divided  into  two  or  more 
equal  parts,  each  of  these  parts  is  called  a  fraction 
of  the  thing  which  is  divided. 

3.  A  fraction,  as  well  as  a  whole  number,  may  be 
expressed   by  figures.     Each  fraction  is  usually  ex- 
pressed by  means  of  two  numbers,  one  written  above 
the  other,  with  a  line  between  them  ;  thus, 


one  half. 
.  one  third. 
.  two  thirds. 
.  one  fourth. 
.  two  fourths, 
three  fourths. 

one  fifth. 
.  two  fifths. 


3-,  .  .     .     .      one  sixth. 

f ,  .  .     .     .   five  sixths. 

f ,  .  .     .     .     six  sixths. 

f ,  .  .     .  three  sevenths. 

f ,  .  .  .  nine  eighths. 

H>  •  .  eleven  twelfths. 

|f,  .  .  nineteen  -twelfth*. 

/y,  .  .  five  twenty-firsts. 


76  '  INTELLECTUAL.  [SEC.  IV. 

4.  The  number  below  the  line  shows  into  how  many 
parts  a  unit  is  divided.      It  is  called    the  DENOM- 
INATOR,   because    it   denominates    or   gives    name  to 
the  parts  ;  thus,  if  an  apple,  or  any  thing,  is  divided  into 
three  equal  parts,  each  part  is  one  third  of  the  apple  or 
thing ;  if  into  eight,  each  part  is  one  eighth. 

5.  The  number  above  the  line  is   called   the  NU- 
MERATOR, because  it  numerates  or  numbers  the  parts 
taken  ;  thus  the  fraction  f,  indicates  that  a  unit  has  been 
divided  into  three  equal  parts,  and  that  two  of  the  parts 
are  used. 

6.  The   numerator   and   the   denominator  are  the 
TERMS  of  the  fraction. 

7.  A  PROPER  FRACTION  is  one  whose  numerator 
is  less  than  its  denominator  ;  as  J,  f ,  £.     The  value 
of  a  proper  fraction  is  less  than  one. 

8.  An  IMPROPER  FRACTION  is  one  whose  numera- 
tor equals  or   exceeds   its    denominator;  as,  |,  f,  f. 
The  value-  of  an  improper  fraction  is  one  or  more 
than  one  ;  for  this  reason  it  is  called  an  improper  frac- 
tion. 

9.  A  MIXED  NUMBER  is  a  whole  number  and  a  frac- 
tion united;  as  2^,  read  two  and  one  half;  5|,  read 
five  and  two  thirds. 

LESSON  II. 

«  «, 

1 .  IN  3  apples  how  many  halves  of  an  apple  ? 
Solution.  There  are   2 'halves  in  1  apple  ;  therefore 

there  are  3  times  2  halves,  which  are  6  halves,  in  3 
apples. 

2.  What  fraction  represents  6  halves  ?     Ans.  f . 

3.  A   man  divided  5  barrels    of  flour   among  his 
workmen,  giving  them  -i-  of  a  barrel  apiece  ;   to  how 

.  many  men  did  he  give  the  flour? 

4.  How  many  halves  are  there  in  5  whole  ones  ? 

5.  A  man  having  3  barrels  and.  1  half  of  a  barrel 
of  apples,  wishes  to  give  them  to  some  poor  people  ; 


LES.  II.]  ARITHMETIC,  77 

to  how  many  can  he  give  them,  if  he  gives  them  \  of 
a  barrel  apiece  ? 

6.  How  many  halves  are  there  in  3  and  1  half  ? 
Solution.  In  3  whole  ones  there  are  3  times  2  halves, 

which  are  6  halves  ;  to  this  add  the  1  half,  and- we  have 
7  halves  or  J ;  therefore,  in  3  and  1  half  there  are  7 
halves. 

7.  A  man  paid  1  half  of  a  dollar  apiece  to  several 
workmen  ;  it  took  4  dollars  and  1  half  of  a  dollar  to 
pay  them  ;  how  many  men  did  he  pay  ? 

8.  How  many  halves  are  there  in  4  and  1  half ; 
that  is,  in  4-J-  ? 

9.  How  many  halves  are  there  in  1  ?     In  2  ?     In 
3?   In  4?   In  5? 

10.  How  do  you  know  how  many  halves  there  are 
in  any  number  ? 

Ans.  There  are  twice  as  many  halves  as  there  are 
whole  ones,  because  it  takes  two  halves  to  make  one 
whole  one. 

11.  In  6  melons  how  many  half  melons  ? 

12.  In  $8  how  many  half  dollars  ? 

13.  Change  9  to  halves. 

14.  Change  6  and  1  half  to  halves. 

15.  Change  7J-  to  halves. 

16.  Change  12^  to  halves. 

17.  If  you  cut  2  melons  each  into  3  equal  pieces,* 
how  many  pieces  will  you  -have  ?     What   part  of  a 
melon  will  each  piece  be  ? 

18.  If  you  cut  3  apples  each  into  3  equal  piccop, 
how  many  pieces  will  they  make  ?     What  part  of  an 
apple  will  each  piece  be  ? 

19.  If  you  cut  4  pies  each  into  3  equal  pieces,  how 
many  pieces  will  they  make  ? 

20.  How  many  thirds  are  there  in  1  ?    In  2  ?    In 
3  ?    In  4  ?    In  5  ?    In  9  ? 

21.  How  do  you  know  how  many  thirds  theje  are 
in  any  number? 


78  INTELLECTUAL  [SEC.  IV. 

Ans.  There  are  3  times  as  many  thirds  as  there  are 
whole  ones,  because  it  takes  three  thirds  to  make  one 
whole  one. 

22.  I  have  1  cord  and  1  third  of  a  cord  of  wood  to 
give  to  some  poor  persons ;  to  how  many  can  I  give  it, 
if  I  give  them  1  third  of  a  cord  apiece  ? 

23.  How  many  thirds  are  there  in  1^? 

24.  A  man  gave  3  dollars  and  2  thirds  of  a  dollar 
to  some  poor  persons,  giving  them  1  third  of  a  dollar 
apiece  ;  to  how  many  persons  did  he  give  it  ? 

25.  How  many  thirds  are  there  in  3§  ? 

26.  How  many  thirds  in  5J?     In    7f  ?     In  11§  ? 
In  12J  ? 

27.  If  a  boy  eats^l  fourth  of  a  pie  at  a  meal,  how 
many  boys,  at  the  same  rate,  will  eat  a  whole  pie  at  a 
meal  ?     How  many  boys  will  eat  2  pies  ?    3  pies  ?    4 
pies  ?    6  pies  ? 

28.  How  many  fourths  are  there  in  1  ?     In  2  ?   3  ? 
4?   6?   8? 

29.  How  do  you  know  how  many  fourths  there  are 
in  any  number  ? 

30.  If  a  horse  will  eat  1  fourth  of  a  bushel  of  oats 
in  a  day,  in  how  many  days  will  he  eat  a  bushel  ?    2 
bushels  ?    2  bushels  and  J  of  a  bushel  ?    3£  bushels  ? 
5  £  bushels  ? 

31.  How  many  fourths  are  there  in  2  and  3  fourths  ? 
In3J?     In5J?     In7J?     In  7J  ? 

32.  If  a  boy  can  earn  1  fifth  of  a  dollar  in  a  day, 
in  how  many  days  can  he  earn  1  dollar  ?     2  dollars  ? 
3  dollars?    6  dollars?    8  dollars? 

33.  How  many  fifths  are  there  in  1  ?     In  2  ?     3  ? 
5?    10? 

34.  How  do  you  know  how  many  fifths  there  are 
in  any  number? 

35.  If  a  boy  can  earn  1  fifth  of  a  dollar  in  a  day, 
how  many  boys  will  it  take  to  earn  1  dollar  and   I 
fifth  of  a  dollar  in  the  same  time  ?     How  many  to 


LES.  II.]  ARITHMETIC.  79 

earn  2  dollars  and  3  fifths  of  a  dollar  ?  4  dollars  and 
2  fifths  of  a  dollar  ?     of  dollars  ?     $7f  ? 

36.  How  many  fifths  are  there  in  1  and  1  fifth  ? 
In  2  and  3  fifths  ?     In  4f  ?     In  5f  ?     In  8f  ? 

37.  In  6  dollars  and  2  fifths  of  a  dollar  how  many 
fifths  of  a  dollar? 

38.  In  6  and  2  fifths  how  many  fifths? 

39.  In  7  and  3  fifths  how  many  fifths  ? 

40.  In  9  and  4  fifths  how  many  fifths  ? 

41.  If  a  quart  of  strawberries  costs  1  sixth  of  a 
dollar,  how  many  quarts   can    I  buy  for    1    dollar  ? 
For  2  dollars  ?   3  dollars  ?    5  dollars  ?   7  dollars  ? 

42.  How  many  sixths  are  there  in  1  ?     In  2  ?     3  ? 
5?   8?    9? 

43.  How  do  you  know  how  many  sixths  there  are 
in  any  number  ? 

44.  In  2  and  1  sixth  how  many  sixths  ? 

45.  In  3  and  5  sixths  how  many  sixths  ? 

46.  In  5  and  3  sixths  how  many  sixths  ? 

47.  In  6  and  4  sixths  how  many  sixths  ? 

48.  How  many  sevenths  are  there  in  1  ?     In  2  ? 
3?   5?   7?   9?   10? 

49.  How  many  sevenths  in  1  and  3  sevenths  ? 

50.  How  many  sevenths  in  1  and  6  sevenths  ? 

51.  How  many  sevenths  in  2  and  4  sevenths  ? 

52.  How  many  sevenths  in  3  and  3  sevenths  ? 

53.  How  many  sevenths  in  5  and  2  sevenths  ? 

54.  How  many  sevenths  in  9  and  6  sevenths  ? 

55.  How  many  eighths  inl?     In2?3?5?7? 
10?    12? 

56.  In  3  and  5  eighths  how  many  eighths  ? 

57.  In  5  and  3  eighths  how  many  eighths  ? 

58.  In  9  and  7  eighths  how  many  eighths  ? 

59.  How  many  ninths  are  there  in  1  ?     In  2  ?   3  ? 
5?   4?   8?   7? 

60.  In  2  and  5  ninths  how  many  ninths  ? 

61.  In  3  and  8  ninths  how  many  ninths  ? 


80  INTELLECTUAL  [SEC.  IV. 

62.  In  5  and  4  ninths  how  many  ninths  ? 

63.  In  7  and  7  ninths  how  many  ninths  ? 

0  L  How  many  tenths  in  1  ?     In   2  ?    3  ?    6  ?    9  ? 

65.  In  2  and  3  tenths  how  many  tenths  ? 

66.  In  3  and  7  tenths  how  many  tenths  ? 

67.  In  5  and  2  tenths  how  many  tenths  ? 

68.  In  4  and  5  sixths  how  many  sixths  ? 

69.  In  5  and  1  seventh  how  many  sevenths  ? 

70.  In  9  and  2  fifths  how  many  fifths  ? 

71.  In  4|  how  many  times  £? 

72.  In  5f\  how  many  times  ^  ? 

73.  In  2^  how  many  times  ^  ? 

74.  In  3y\  how  many  elevenths  ? 

75.  In  6J  how  many  fifths  ? 

LESSON  III. 

1.  IF  you  give  2  boys  1  half  of  an  apple  apiece, 
how  many  apples  will  it  take  ? 

2.  If  you  give  4  men  1  half  of  a  dollar  apiece, 
how  many  dollars  will  it  take  ? 

3.  In  4  halves  how  many  whole  ones  ? 

4.  In  6  halves  how  many  times  1  ? 

5.  In  8  halves  how  many  times  1  ? 

6.  How  do  you  know  how  many  whole  ones  there 
are  in  any  number  of  halves  ? 

Ans.  Since  it  takes  two  halves  to  make  one  whole 
one,  there  will  be  as  many  whole  ones  as  2  is  con- 
tained times  in  the  given  number  of  halves ;  or,  there 
will  be  half  as  many  whole  ones  as  there  are  halves. 

7.  What  is  one  half  of  8  ?     One  half  of  10  ?     Of 
20  ?     Of  24  ?     Of  30  ?     See  page  48. 

8.  If  you   give  3  boys  1  half  of  a  melon  apiece, 
how  many  melons  will  it  take  ? 

9.  What  is  1  half  of  3  ?     Ans.  Three  halves  =  U. 
10.  If  you  give  5  poor  people  1  half  of  a  barrel  of 

flour  apiece,  how  many  barrels  will  it  take  ? 


LES.  III.]  ARITHMETIC.  81 

11.  In  5  halves  how  many  whole  ones  ? 

12.  What  is  £  of  5  ?     Ans.  5  halves  =  2  J. 

13.  If  the  interest  of  $1  is  J  of  a  cent  per  month, 
what  is  the  interest  of  the  same  sum  for  7  months  ? 
For  8  months  ?     For  9  months  ?     For  1 1  months  ? 

14.  In  7  halves  how  many  times  1  ? 

15.  In  9  halves  how  many  times  1  ? 

16.  What  is  J-  of  9?     Of  11?   15  ?   21  ?   25  ? 

17.  A  boy  divided  some  oranges  among  6  of  his 
companions,  giving  1  third  of  an  orange  to  each ;  how 
many  oranges  did  it  take  ? 

18.  In  6  thirds  how  many  whole  ones  ? 

19.  What  is  £  of  6  ?     Ans.  6  thirds  =  2. 

20.  A  teacher  visited  9  different  schools,  spending  1 
third  of  a  day  in  each ;  how  many  days  did  it  take  ? 

21.  In  9  thirds  how  many  tunes  1  ? 

22.  What  is  J  of  9  ? 

23.  A  man  divided  some  coal  among  7  poor  families, 
giving  1  third  of  a  ton  to  each  family  ;  how  many  tons 
did  it  take  ? 

24.  In  7  thirds  how  many  times  1  ? 

25.  What  is  £  of  7  ? 

26.  A  boy  gave  1  third  of  a  pineapple  to  each  of 
his  12  playmates  ;  how  many  pineapples  did  it  take  ? 

27.  In  12  thirds  how  many  times  1  ? 

28.  How  do  you  know  how  many  whole  ones  there 
are  in  any  number  of  thirds  ? 

29.  What  is  Jof  12?     Of  10?   15?   20? 

30.  If  a  man  spends  1  fourth  of  a  dollar  in  1  day, 
how  many  dollars  will   he  spend  in  4  days?     In  8 
days  ?    12  days  ?   20  days  ? 

31.  In  8  fourths  how  many  times  1  ? 

32.  In  20  fourths  how  many  times  1  ? 

33.  How  do  you  know  how  many  whole  ones  there 
are  in  any  number  of  fourths  ? 

34.  What  is  i  of  4?     Of  8?     Ofl6?Of24?Of 
32  ?     Of  40  ? 

6 


82  INTELLECTUAL  [SEC.  IV. 

35.  A  benevolent  lady  gave  1  fourth  of  a  dollar 
apiece  to  9  poor  children ;  how  many  dollars  did  it  take  ? 

36.  In  |  how  many  times  1  ?     Ans.  2£. 

37.  In  7  fourths  how  many  times  1  ? 

38.  In  11  fourths  how  many  times  1  ? 

39.  In  17  fourths  how  many  times.  1  ? 

40.  What  is  i  of  7?     Of  11  ?     Of  17?    Of  23? 

41.  If  1  fifth  of  a  ton  of  coal  will  supply  a  furnace 
1  week,  how  many  tons  will  supply  it  10  weeks  ?   20 
weeks  ?    15  weeks  ?    25  weeks  ? 

42.  In  10  fifths  how  many  times  1  ? 

43.  In  8  fifths  how  many  times  1  ? 

44.  In  12  fifths  how  many  times- 1  ? 

45.  In  19  fifths  how  many  times  1  ? 

46.  If  the  interest  of  $1  is  £  of  a  mill  for  1  day, 
what  is  the  interest  of  $1  for  6  days  ?     For  18  days  ? 
For  9  days  ?     For  20  days  ? 

47.  What  is  £  of  6?     Of  18?     Of  9?     Of  20? 

48.  In  15  sixths  how  many  times  1  ? 

49.  In  24  eighths  how  many  times  1  ? 

50.  In  27  tenths  how  many  times  1  ? 

51.  In  21  sevenths  how  many  times  1  ? 

52.  In  48  ninths  how  many  times  1  ? 

53.  In  45  fifths  how  many  times  1  ? 

54.  In  27  twelfths  how  many  times  1  ? 

LESSON  IV. 

1.  IF  it  takes  1  third  of  an  hour  to  walk  1  mile, 
how  long  will  it  take  to  walk  2  miles  ? 

2.  What  is  2  times  1  third  ? 

3.  If  the  interest  of  1  dollar  is  1  half  of  a  cent 
for  1  month,  what  is  the  interest  of  2  dollars  for  the 
same  time  ?     What  the  interest  of  3  dollars  ?  -  Of  4 
dollars  ?     Of  7  dollars  ?     Of  10  dollars  ? 

4.  What  is  2  times  1  half?     3  times  1  half?     4 
times  1  half  ?     7  times  £  ?     10  times  J  ? 


L:;s.  IV.]  ARITHMETIC.  83 

5.  If  1  pound  of  coffee  costs  1  fourth  of  a  dollar, 
what  will  3  pounds  cost  ? 

6.  What  is  three  times  1  fourth  ? 

7.  When  potatoes  are  worth  3  fourths  of  a  dollar 
a  bushel,  how  many  fourths  of  a  dollar  will  2  bushels 
cost  ?     How  many  dollars  ? 

8.  Two   times  f  are  how  many   fourths  ?     How 
many  times  1  ? 

9.  If  a  dinner  for  1  man  costs  2  thirds  of  a  dollar, 
what  will  a  dinner  for  4  men  cost? 

10.  Four   times   |-  are   how  many   thirds  ?     How 
many  times  1  ? 

11.  When  eggs-  are  worth  1  fifth  of  a   dollar   a 
dozen,  what  are  3  dozen  worth  ? 

12.  What  is  3  times  1  fifth? 

13.  Charles  earned  2  fifths  of  a  dollar  on  Monday  ; 
at  the  same  rate  per  day  how  many  fifths  of  a  dollar 
does  he  earn  in  the  week?     How  many  dollars  ? 

14.  Six  times  f  are  how  many  fifths?     How  many 
times  1  ? 

15.  If  1  bushel  of  oats  costs  3  fifths  of  a  dollar,  what 
shall  I  pay  for  7  bushels  ? 

16.  Seven  times   f  are  how  many  fifths?     How 
many  times  1  ? 

17.  When    corn   is  worth  4  fifths  of  a   dollar   a 
bushel,  what  will  6  bushels  cost? 

18.  Six  times  4  fifths  are  how  many  fifths  ?     How 
many  times  1  ? 

19.  If  the  interest  of  1  dollar  is  1  sixth  of  a  mill 
for  1  day,  what  is  the  interest  of  5  dollars  for  the  same 
time  ?     What  the  interest  of  9  dollars  ? 

20.  What  is  '5  times  J-  ?    9  times  %  ? 

21.  If  the  interest  of  $1   is  1  sixth  of  a  mill  per 
day,  what  is  the  interest  of  the  same  sum  for  5  days  ? 
For  15  days  ?     For  12  days  ? 

22.  If  the  interest  of  $1  for  1  day  is  1  sixth  of  a 
mill,  what  is  the  interest  of  $3  for  4  days  ? 


84  INTELLECTUAL  [SEC.  IV. 

23.  Four  times  3  sevenths  are  how  many  sevenths  ? 
How  many  times  1  ? 

24.  Eight  times  3  fourths  are  how  many  fourths  ? 
How  many  times  1  ? 

25.  What  is  6  times  4  fifths  ? 

26.  What  is  4  times  5  sixths  ? 

27.  What  is  3  times  4  ninths  ? 

28.  What  is  6  times  4  sevenths  ? 

29.  What  is  9  times  3  eighths  ? 

30.  What  is  5  times  9  tenths  ? 

31.  What  is  8  times  3  elevenths  ? 

32.  What  is  6  times  f  ? 

33.  What  is  4  times  f  ? 

34.  What  is  7  times  f  ? 

35.  What  is  9  times  f  ? 

36.  What  is  8  times  J  ? 

37.  What  is  5  times  |? 


LESSON  V. 

1.  IF  corn  is  worth  a  dollar  and  a  half  a  bushel, 
what  shall  I  pay  for  2  bushels  ? 

2.  When  apples  cost  two  dollars  and  a  half  a  bar- 
rel, what  will  3  barrels  cost  ? 

3.  How  many  are  3  times  2  and  1  half? 
Solution.  Three  times  2  are  6,  and  3  times  1  half 

are  3  halves,  or  1  and  1  half,  which,  added  to  6,  gives 
7  and  1  half;  therefore  3  times  2J  are  7^. 

4.  If  a  barrel  of  flour  costs  6  dollars  and  a   half, 
what  will  5  barrels  cost  ? 

5.  How  many  are  5  times  6  and  1  half? 

6.  What  are  8  yards  of  cloth  worth,  at  3  dollars 
and  a  half  per  yard  ? 

7.  How  many  are  8  times  3  and  1  half  ? 

8.  If  white  lead  is  worth  9  dollars  and  1  third  per 
hundred  weight,  what  are  2  hundred  weight  worth  ? 

9.  How  many  are  twice  9  and  1  third  ? 


LES.  V.]  ARITHMETIC.  85 

10.  When  nails  are  worth  6  cents  and  2  thirds  per 
pound,  what  are  9  pounds  worth  ? 

11.  How  many  are  9  times  6  and  2  thirds  ? 

12.  How  many  are  7  times  3  and  2  thirds  ? 

13.  How  many  are  8  times  4  and  1  third  ? 

14.  When  flour  costs  7  dollars  and  3  fourths  per 
barrel,  what  will  5  barrels  cost  ? 

15.  How  many  are  5  times  7  and  3  fourths  ? 

16.  When  apples  cost  3  dollars  and  1  fourth  per 
barrel,  what  must  I  pay  for  8  barrels  ? 

17.  How  many  are  8  times  3  and  1  fourth  ? 

18.  How  many  are  3  times  8  and  1  fourth? 

19.  How  many  are  5  times  11  and  3  fourths  ? 

20.  If  raisins  cost  3  dollars  and  2  fifths  per  box, 
what  will  2  boxes  cost  ? 

21.  How  many  are  2  times  3  and  2  fifths? 

22.  How  many  are  5  times  4  and  3  fifths  ? 

23.  How  many  are  3  times  9  and  3  fifths  ? 

24.  If  1  man  earns  1  dollar  and  5  sixths  in  a  day, 
how  much  will  8  men  earn  in  the  same  time  ? 

25.  How  many  are  8  times  1  and  5  sixths  ? 

26.  How  many  are  9  times  4  and  1  sixth  ? 

27.  How  many  are  6  times  7  and  3  sixths  ? 

28.  If  1  man  earns  2  dollars  and  1  sixth  in  1  day, 
how  much  will  3  men  earn  in  4  days  ? 

29.  If  12  yards  and  3  sevenths  of  a  yard  of  silk 
are  required  to  make  1  dress,  how  many  yards  will  be 
required  for  5  dresses  ? 

30.  How  many  are  5  times  12  and  3  sevenths? 

31.  What  cost  2  barrels  of  beef,  at  18  dollars  and  5 
eighths  per  barrel  ? 

32.  How  many  are  2  times  18  and  5  eighths? 

33.  How  many  are  3  times  16  and  5  ninths  ? 

34.  How  many  are  4  times  20  and  3  eighths  ? 

35.  In  an  orchard  of  10  trees,  each  tree  bears  9 
bushels  and  5  eighths  of  a  bushel  of  apples  ;  how  many 
bushels  does  the  whole  orchard  bear  ? 


86  INTELLECTUAL  [SEC.  IV. 

36.  If  it  takes  2  yards  and  3  eighths  of  a  yard  of 
cloth  to  make  a  coat,  and  1  yard  and  5  eighths  to  make 
a  pair  of  pantaloons,  how  many  yards  will  it  take  to 
make  5  coats  and  5  pair  of  pantaloons  ? 

37.  If  3  men  can  do  a  piece  of  work  in  5  days  and 
4  ninths  of  a  day,  how  many  days  will  it  take  1  man 
to  do  the  same  ? 

38.  If  3  men  can  build  4  rods  and  5  sixths  of  a  rod 
of  wall  in  1  day,  how  many  rods  can  they  build  in  5 
days  ?     In  4  days  ? 

00.  How  many  are  5  times  4f  ? 

Solution.  Five  times  4  are  20,  and  5  times  f  are  -\£, 
or  4  and  £,  which,  added  to  20,  make  24£ ;  there- 
fore, 5  times  4f  are  24-J-. 

40.  How  many  are  4  times  4f  ? 

Solution.  Four  times  4  are  16,  and  4  times  g  are 
-2<;°-,  or  3.\,  which,  added  to  16,  make  1(JJ  ;  there- 
fore, 4  times  4J  are  11K\  ? 

41.  How  many  are  4  times  2  J  ? 

42.  How  many  are  3  times  4|  ? 

43.  How  many  are  5  times  3|  ? 

44.  How  many  are  4  times  3J  ? 

45.  How  many  are  4  times  3g  ? 

46.  How  many  are  6  times  2|  ? 

47.  How  many  are  9  times  5  J  ? 

LESSON  VI. 

1.  IF  you  divide  a  barrel  of  flour  equally  between 
2  persons,  what  part  of  a  barrel  will  each  have  ? 

2.  If  you  divide  a  melon  equally  among    3  boys, 
what  part  of  a  melon  will  you  give  to  each  boy  ? 

3.  How  can  you  divide  2  melons  equally  among  3 
boys? 

Ans.  Divide  each  melon  into  3  equal  pieces,  and 
then  give  each  boy  1  piece  from  each  melon  ? 

4.  What  is  1  third  of  2  ?     Ans.  2  thirds  of  1. 


LKS.  VI.]  ARITHMETIC.  87 

5.  What  is  1  third  of  4?     Am.  4  thirds  =  1J. 

G.  What  is  l  third  of  5  ? 

7.  If  3  yards  of  silk  cost  4  dollars,  what  is  the 
price  of  1  yard  ? 

8.  If  3  bushels  of  wheat  cost  $5,  what  is  the  price 
per  bushel  ? 

9.  What  is  J  of  7  ?     Of  8  ?     Of  10  ?     Of  11  ? 

10.  If  a  barrel  of  flour  is  divided  equally  among  4 
persons,  what   part  of  a  barrel   does  each  receive  ? 
What  would  each  receive  if  2  barrels  were  divided  ? 
What  if  3  barrels  ?     If  5  barrels  ?     If  6  barrels  ? 

11.  What  is  1  fourth  of  2  ?     Am.  f,  or  \. 

12.  What  is  1  fourth  of  3? 
Ans.  3  fourths  of  1,  or  f . 

(   13.  What  is  1  fourth  of  5  ?    Of  6  ?    Of  7  ?    Of  9  ? 

14.  If  5  boys  eat  a  bushel  of  apples  in  a  week,  what 
part  of  a  bushel  will  1  boy  eat  in  the  same  time  ? 
Wiiat  will  2  boys  eat  ?     3  boys  ?     4  boys  ?     6  boys  ? 

15.  What  is  i  of  2  ?     Ans.  f  of  1. 

16.  What  is  i  of  3  ?     Of  4  ?    6  ?   9  ?    12  ? 

17.  What  is  J-  of  2  ?     Of  3  ?   4  ?   5  ?   8  ?   9  ?   10? 
11?    15? 

18.  What  is   \   of  2?    3?    4?    5?    6?    8?    9? 
13?   15? 

19.  What  is  \  of  2  ?   3  ?   4  ?  5  ?   6  ?   7  ?   9  ?   12  ? 

20.  What  is  J  of  2  ?   3  ?   4  ?   5  ?    6  ?   7  ?   8  ?   10  ? 
11?   12? 

21.  What  is   ^of  2?   3?    4?    5?   8?   9?   10? 

22.  What  is  ^  of  2  ?    6?   9?    12?    14?    15? 

23.  What  is  -j^  of  2  ?  3  ?   4  ?   5  ?   6  ?   7  ?   8  ?   9  ? 
10?   11?    12?   15?    18?   20? 

24.  What  is  2  thirds  of  2  ? 

Solution.  One  third  of  2  is  2  thirds  of  1,  and  two 
thirds  of  2  are  2  times  2  thirds,  which  are  4  thirds,  or  1 
and  1  third;  therefore,  2  thirds  of  2  is  1£. 

25.  If  1  barrel  of  apples  cost  $2,  what  will  1  third 
of  a  barrel  cost  ?     What  2  thirds  of  a   barrel  ? 


88  INTELLECTUAL  [SEC.  IV. 

2G.  If  a  cord  of  wood  costs  $5,  what  will  1  fourth 
of  a  cord  cost  ?  What  will  3  fourths  of  a  cord  cost  ? 

27.  What  is  j  of  5  ?     See  Ex.  24. 

28.  If  4  bushels  of  corn  cost  $3,  what  will  1  bushel 
cost  ?     What  will  3  bushels  cost  ?     5  bushels  ? 

29.  What  is  }  of  3  ?   £  of  3  ? 

30.  If  a  box  of  lemons  costs  $4,  what  will  J  of  a 
box  cost?    f  of  a  box  ?    f  ?    £  ? 

31.  What  is  J-  of  4?   £of  4?   f?   f? 

32.  If  7  gallons  of  molasses  cost  5  dollars,  what 
will  1  gallon  cost  ?   2  gallons  ?   3  gallons  ?   5  gallons  ? 
8  gallons  ? 

33.  What  is  }  of  5  ?    f  of  5  ?    $  of  5  ?    |  ?   f  ? 

*?   f  ? 

34.  If  8  gallons  of  vinegar  are  wor.th  2  dollars, 
what  is  1  gallon  worth  ?     What  are  2  gallons  worth  ? 
3  gallons?    5  gallons?    7  gallons?    9  gallons? 

3").  What  is  £  of  2?    f  of  2  ?   f?   fc?   f? 

36.  If  6  yards  of  satinet  cost  5  dollars,  what  is  the 
cost  of  1  yard  ?     Of  2  yards  ?    3  yards  ?   4  yards  ? 
5  yards  ? 

37.  What  is  J  of  5  ?   f  of  5  ?  f  of  5  ?   f  ?   -J  ?   §  ? 
*   38.  What  is  |  of  8  ?   §  of  9  ?   f  of  7  ?   f  of  11  ? 
|  of  10  ? 

39.  If  5  yards  of  cloth  cost  $12,  what  will  1  yard 
cost  ?    2   yards  ?    3  yards  ?    4  yards  ?    6   yards  ?    8 
yards  ? 

40.  What  is  f  of  17  ? 

Solution.  One  fifth  of  17  is  3f,  and  fAra?  fifths  are 
3  times  3f ;  3  times  3  are  9,  and  3  times  f  are  f ,  or 
1 J,  which,  added  to  9,  makes  10£  ;  therefore,  etc. 

NOTE.  This  method  is  best  for  largo  ptftabors,  and  that 
given  in  Ex.  24  is  best  for  small  numbers. 

41.  What  is  7  fifths  of  17  ? 

42.  •  What-  is  3  sevenths  of  24  ? 

43.  What  is  7  ninths  of  20? 

44.  What  is  f  of  19  ?    f  of  21  ?    f  of  26  ? 


LES.  VII.]  ARITHMETIC.  80 

45.  What  is  £  of  15  ?-  ^  of  18  ?   -ft  of  26  ? 

46.  What  is  ^  of  17  ?    TV  of  19  ?   Y  of  13  ? 

47.  What  is  |  of  24?   f  of  36  ?   J  of  24? 

48.  What  is  T\  of  44  ?    f  of  42  ?    T»T  of  77  ? 

49.  What  is  £  of  27  ?   f  of  49  ?   £  of  81  ? 

50.  What  is  f  of  24  ?   £  of  42  ?   f  of  80  ? 

51.  What  is  T7T  of  33  ?   f  of  40  ?   f  of  63  ? 

52.  What  is  |  of  64?   f  of  63  ?   ^  of  60  ? 


LESSON  VH. 

1.  IF  1  half  of  a  barrel  of  apples  costs  1  dollar 
and  1  third  of  a  dollar,  what  will  a  barrel  cost  ? 

2.  1  and  1  third  is  1  half  of  what  number  ? 
Solution.  Since   1   half  of  the  number  is   1  and  1 

third,  2  halves,  or  the  whole  of  the  number,  will  be  2 
times  1  and  1  third,  which  are  2  and  2  thirds;  there- 
fore, 1  and  1  third  is  1  half  of  2  and  2  thirds. 

3.  If  1  third  of  a  box  of  oranges  costs  2  dollars 
and  1  fourth,  what  will  2  thirds  of  a  box  cost  ?     What 
a  whole  box  ? 

4.  2  and  1  fourth  is  1  third  of  what  number  ? 

5.  .If  1  fourth  of  a  ton  of  hay  costs  3  dollars  and 
1  half,  what  will  2  fourths  of  a  ton  cost  ?     What  will 
3  fourths  of  a  ton  cost  ?     What  a  whole  ton  ? 

6.  3  and  1  half-  is*  1  fourth  of  what  number  ? 

7.  If  1  fifth  of  a  ton  of  coal  costs  1  dollar  and  3 
fourths,  what  will    2  fifths  of  a  ton  cost?     What  3 
fifths  ?    4  fifths  ?    5  fifths,  or  a  whole  ton  ? 

8.  1  and  3  fourths  is  1  fifth  of  what  number  ? 

9.  If  1  sixth  of  a  barrel  of  flour   costs  1  dollar 
and  3  fifths,  wjiat  will  2  sixths  of  a  barrel  cost  ?    3 
sixths  ?    4  sixths  ?    5  sixths  ?    6  sixths,  or  a  whole  bar- 
rel? 

10.  1  and  3  fifths. is  1  sixth  of  what  number?  ' 

11.  If  a  man  can  walk  4  miles  and  5  sixths  of  a 
mile  in  1  seventh  of  a  day,  how  far  can  he  walk  in  2 


90  INTELLECTUAL  [SEC.  IV- 

sevenths  of  a  day  ?  In  3  sevenths  ?  In  4  sevenths  ? 
In  a  whole  day  ? 

12.  4  and  5  sixths  is  1  seventh  of  what  number? 

l'>.  A  boy  skated  1  mile  and  5  sevenths  in  1  eighth 
of  an  hour ;  how  far,  at  the  same  rate,  would  he  skate 
in  2  eighths  of  an  hour?  In  3  eighths?  In  5 
eighths  ?  In  an  hour  ? 

14.  1  and  5  sevenths  is  1  eighth  of  what  number? 

15.  A  locomotive  ran  3  miles  and  2  fifths  of  a  mile 
in  1   ninth  of  an   hour ;  how  far  would  it  run  in   2 
ninths  of  an  hour  ?     How  far  in  3  ninths  of  an  hour  ? 
In  4  ninths  ?     In  6  ninths  ?     In  an  hour  ? 

16.3  and  2  fifths  is  1  ninth  of  what  number  ? 

17.  A  ship  sailed  1  mile  and  1  fourth  in  1  tenth  of 
an  hour ;  how  far  would  she  sail  in  2  tenths  of  an 
hour  ?    How  far  would  she  sail  in  3  tenths  of  an  hour  ? 
In  4  tenths  ?     In  5  tenths  ?    In  9  tenths  ?     In  an  hour  ? 

18.  1  and  1  fourth  is  1  tenth  of  what  number? 

19.  6  and  2  fifths  is  1  seventh  of  what  number? 

20.  4  and  3  sevenths  is  1  fifth  of  what  number  ? 

21.  5  and  3  fourths  is  1  eighth  of  what  number  ? 

22.  6  and  5  eighths  is  1  fourth  of  what  number? 

23.  3  and  f  is  ^  of  what  number  ? 

24.  4  and  f  is  T\y  of  what  number  ? 

25.  3  and  §  is  £  of  what  number  ? 

26.  of  is  }2  of  what  number  ? 

27.  2£  is  ^  of  what  number? 

28.  3f  is  ^  of  what  number  ? 

29.  If  2  thirds  of  a  box  of  lemons  cost  3  dollars, 
what  will  one  third  of  a  box  cost  ?     What  will  a  box 
cost? 

30.  3  is  2  thirds  of  what  number  ? 

/Solution.  Since  3  is  two  thirds,  one  third  is  1  half 
of  3,  which  is  1  and  1  half;  and  three  thirds,  or  the 
whole,  will  be  three  times  1  and  1  half,  which  are  4  and 
1  half ;  therefore,  3  is  2  thirds  of  4  and  1  half. 

31.  5  is  2  thirds  of  what  number? 


LES.  VII.]  ARITHMETIC.  91 

32.  If  3  fourths  of  a  yard  of  cloth  cost  $4,  what 
will  1  fourth  of  a  yard  cost  ?     What  will  a  yard  cost  ? 

33.  If  4  is  3  fourths  of  some  number,  what  is  1 
fourth  of  the  same  number  ?     1  and  1  third  is  1  fourth 
of  what  number  ?  Then  4  is  3  fourths  of  what  number  ? 

34.  If  f  of  a  box  of  lemons  cost  $3,  what  will  a 
box  cost? 

35.  If  3  is  f  of  some  number,  what  is  £  of  the  same 
number?    1J  is  J  of  what  number?     Then  3  is  f  of 
what  number  ? 

36.  If  |  of  a  hundred  weight  of  sugar  cost  $8,  what 
will  1  hundred  weight  cost  ? 

37.  If  8  is  f  of  some  number,  what  is  J  of  the  same 
number  ?  If  is  ^  of  what  number  ?     Then  8  is  ^  of 
what  number? 

38.  If  J  of  a  cord  of  wood  cost  $4,  what  will  a  cord 
cost? 

39.  4  is  f  of  what  number  ? 

40.  If  ^  of  a  ton  of  hay  cost  $16,  what  will  a  ton 
cost? 

41.  16  is  y7^  of  what  number  ? 

42.  If  a  man  can  earn  $23  in  -fy  of  a  month,  what 
can  he  earn  in  a  month  ? 

43.  23  is  ^\j  of  what  number  ? 

44.  A  man  can  do  J  of  a  piece  of  work  in  5  days ; 
how  long  will  it  take  him  to  do  the  whole  of  it  ? 

45.  5  is  f  of  what  number  ? 

46.  A  horse  traveled  4  miles  in  £  of  an  hour  ;  how 
far,  at  the  same  rate,  would  he  travel  in  an  hour  ? 

47.  4  is  $  of  what  number  ? 

48.  If  7  pounds  of  flour  cost  38  cents,  whnt  will  12 
pounds  cost? 

49.  38  is  ^  of  what  number  ? 

50.  If  6  yards  of  cloth  costs  $10,  what  will  5  yards 
cost  ?    8  yards  ? 

51.  If  3  men  can  do  a  piece  of  work  in  7  hours, 
how  long  will  it  take  5  men  to  do  the  same  work  ? 


02  INTELLECTUAL.  [SEC.  IV. 

52.  If  2  pipes  will  empty  a  cistern  in  7  hours,  in 
what  time  will  5  pipes  empty  it  ?    3  pipes  ? 

53.  7  is  f  of  what  number  ? 

54.  9  is  £  of  what  number  ? 

55.  18  is  J  of  what  number  ? 

56.  23  is  ^  of  what  number? 

57.  A  man  bought  1  barrel  and  1  fourth  of  a  bar- 
rel of  oil  for  $32  ;  what  was  the  price  per  barrel  ? 

Solution.  A  barrel  and  a  fourth  of  a  barrel  are  the 
same  as  5  fourths  of  a  barrel.  Since  5  fourths  of  a 
barrel  cost  32  dollars,  1  fourth  costs  1  fifth  of  32  dollars, 
which  is  6  dollars  and  2  fifths,  and  4  fourths  cost  4 
times  6  dollars  and  2  fifths,  which  are  25  dollars  and 

3  fifths  of  a  dollar  ;  therefore,  etc. 

58.  A  man  bought  1  acre  and  3  fourths  of  an  acre 
of  land  for  $75  ;  what  was  the  price  per  acre? 

59.  75  is.  J  of  what  number  ? 

60.  Bought  22   yards  of  cloth  for  $12;  what  was 
the  price  per  yard  ? 

61.  12  is  J^-  of  what  number? 

62.  Bought  12  tons  of  hay  for  $30  ;  what  was  the 
price  of  I  ton  ? 

63.  Paid  $18  for  If  barrels  of  cranberries,  what 
did  I  pay  for  1  barrel  ? 

64.  Paid  $7  for  If  boxes  of  raisins;  what,  at  the 
same  rate,  should  I  pay  for  2  boxes  ? 

65.  Twice  T7g  of  7  are  how  many  ? 

66.  Paid  $3" for  If  bushels  of  wheat;  what  would 
3  bushels  cost  ? 

67.  3  times  T8T  of  3  are  how  many  ? 

68.  Bought    1^   barrels   of  apples  for  $4;  what 
should  I  pay  for  4  barrels  ? 

69.  4  times  }%  of  4  are  how  many  ? 

70.  Bought  l^y  gallons  of  vinegar  for  33    cents ; 
what  would  be  the  cost  of  2  gallons  ? 

71.  2  times  ^J  of  33  are  how  many  ? 

72.  5  times  f  of  21  are  how  many  ? 


LES.  I.]  ARITHMETIC.  93 

SECTION   FIFTH. 
LESSON  I. 

UNITED  STATES  MONEY,  sometimes  called  Federal 
Money,  is  the  Currency  of  the  United  States. 

TABLE. 

10  Mills  (m.)                           make  1  Cent,  marked  c. 

10  Cents                                         "      1  Dime,  "        d. 

10  Dimes                                      "      1  Dollar,  "       ft. 

10  Dollars                                   "      1  Eagle,  "       e. 

NOTE.  The  words  eagle  and  dime  are  seldom  or  never  used  in 
business  transactions.  Dollars  and  cents  are  usually  separated 
by  a  point ;  thus,  $36.42  is  read,  36  dollars  and  42. cents. 

TABLE  OF  ALIQUOT  OR  EXACT  TARTS  OF  A  DOLLAR. 

50  cents  =  1  of  a  dollar,  20  cents  =  ^  of  a  dollar, 
331  cents  =  J  of  a  dollar,  16f  cents  =  4  of  a  dollar, 
25  cents  =  4-  of  a  dollar,  124  cents  =  i  of  a  dollar. 

4  '  A  .  O 

1.  How  many  cents  in  2  dimes  ?     In  3  dimes  and 
G  cents  ? 

2.  How  many  cents  in  30  mills  ?     In  45  mills  ? 

3.  Change  $4  and  6  dimes  to  dimes.     $1,  2  dimes, 
and  5  cents  to  cents. 

4.  How  many  cents  in  ^  of  a  dollar  ?     In  £  ?   £  ? 

*?  t?  *?  TV? 

5.  What  will  6  bushels  of  apples  cost,  at  33  J-  cents 
per  bush$  ? 

Solution.  Since  1  bushel  costs  1  third  of  a  dollar,  G 
bushels  will  cost  G  times  1  third  of  a  dollar,  which  arc 
6  thirds  of  a  dollar,  or  2  dollars. 

G.*  At  16f  cents  per  pound,  what  will  9  pounds  of 
raisins  cost  ? 

7.  At  25  cents  per  pound,  what  will  20  pounds  of 
coffee  cost? 

8.  At  12^  cents  a  pound,  what  will  24  pounds  of 
sugar  cost  ? 

9.  Bought  12  sheep,  at  $3.33^  per  head ;  what  did 
they  cost  ? 


94  INTELLECTUAL.  [SEC.  V. 

10.  Bought  5  barrels  of  flour,  at  $9.33£  per  barrel ; 
what  did  I  pay  for  the  lot  ? 

11.  Paid  6J  cents  a  pound  for  12  pounds  of  nails; 
what  did  they  cost  ? 

12.  At  37£  cents  a  yard,  what  will  8  yards  of  rib- 
bon cost  ? 

ENGLISH  OR  STERLING  MONEY  is  the  currency  of 
Great*  Britain. 

TABLE. 

4  Farthings  (qr.)  make  1  Penny,  marked  d. 

12  Pence  "       1  Shilling,  "         s. 

20  Shillings  "      1  1'ound,  "       £. 

NOTE.  A  Sovereign  is  a  gold  coin  equal  to  a  pound.    A 
Guinea  is  21  shillings. 

13.  How  many  farthings  in  2d.  ?     In  3d.    2qr.  ? 

14.  How  many  pence  in  3s.  ?     In  2s.  9d.  ? 

15.  How  many  pounds  in  46s.  ?  In  65s.  ?  In  82s.  6d.? 

16.  Change    l£  2s.  4d.  to  pence.      3£  5s.  6d.    to 
shillings. 

17.  At  5s.  a  yard,  how  many  pounds  will  12  yards 
of  cloth  cost  ?    18  yards  ? 

18.  At   6d.  a  pound,   how  many   shillings  will  18 
pounds  of  cheese  cost  ?    24  pounds  ?    27  pounds  ? 

10.  At  8s.  a  pair,  how  many  pair  of  shoes  may -be 
bought  for  2£  ?  *For  3£  4s.  ? 

LESSON  II. 

TROY  WEIGHT  is  used  in  weighing   gold,  silver, 
and  precious  stones. 

TABLE. 

24  Grains  (gr.)  make  1  Pennyweight,         marked  dwt. 

2»  Pennyweights  "      1  Ounce,  oz. 

12  Ounces  "      1  Pound,  Ib4 

1.  How  many  grains  in  2dwt.  ?     In  2dwt.  6gr.  ? 

2.  How  many  grains  in  2^dwt.  ?     In  1 3 dwt.  ? 

3.  How  many  pennyweights  in  48gr.  ?     In  72gr.  ? 

4.  How  many  pennyweights  in  36gr.  ?     In  42gr.  ? 


LES.  II.]  ARITHMETIC.  05 

5.  How  many  pounds  in    24oz.  ?     In  72oz.  ?     In 
30oz.  ?     In  oloz.  ?     In  69oz.  ? 

6.  How  many  ounces  in  3  Ib.  ?     In  2  Ib.  3oz.  ? 

7.  How  many  dollars  and  cents  will  a  gold  chain 
weighing  12dwt.  cost,  at  9  dimes  per  pennyweight? 

APOTHECARIES'  WEIGHT  is  used  in  mixing  medi- 
cines. 

TABLE. 

20  Grains  (gr.)  make  1  Scruple,          marked  sc.,  or  3. 

3  Scruples  "      1  Dram,  dr.,  or  3 . 
8  Drams                                              1  Ounce,                            oz.,  or   g. 

12  Ounces  "      1  Pound,  "       Ib.,  or  Ib. 

NOTE.  The  pound,  ounce,  and  grain  are  the  same  in  Apoth- 
ecaries' Weight  that  they  are  in  Troy  Weight ;  but  the  ounco 
is  differently  divided. 

8.  How  many  grains  in  29  ?    In  o£)  ogr.  ? 

9.  How  many  scruples  in  40gr.  ?   In  2 ogr.  ? 

10.  How  many  scruples  in  5dr.  ?   In  6dr.  2sc.  ? 

11.  How  many  ounces  in  40dr.  ?    In  4Gdr.  ? 

12.  In  mixing  a   certain   medicine,  an   apothecary 
used  lOgr.  of  one  kind,  2£)  of  another  kind,  and  33  of 
another ;  how  many  grains  did  he  use  in  all  ? 

AVOIRDUPOIS  WEIGHT  is  used  in  weighing  the 
coarser  articles  of  merchandise ;  such  asi  hay,  cotton, 
tea,  sugar,  copper,  iron,  etc. 

TABLE. 

16  Drams  (dr.)                       make  1  Ounce,  marked    oz 

16  Ounces                                    "      1  Pound,  "         ]b. 

25  Pounds                                    "      1  Quarter,  "         qr. 

4  Quarters                                  "      1  Hundred  Weight,  "       cwt. 
20  Hundred  Weight                  "      1  Ton,  t. 

13.  At  9  cents  a  pound,  what  will  Icwt.  of  sugar  cost  ? 

14.  Bought  St.  lOcwt.  of  hay,  at  $12  a  ton ;  what 
was  the  whole  cost  ? 

15.  At  12^  cents  a  pound,  what  will  12  Ib.  of  beef 
cost  ? 

16.  At  16f  cents  a  pound,  what  will  15  Ib,  of  butter 
cost? 

17.  What   cost   24  Ib.   of   honey,   at  33 J   cents   a 
pound  ? 


INTELLECTUAL  [SEC.  V. 

LESSON  LTI. 

CLOTH  MEASURE  is  used  in  measuring  cloth,  rib- 
bons, braids,  etc. 

TABLE. 

2]  Inches  (in.)  make  1  Nail,  marked     na. 

4    Nails  1  (Quarter,  qr. 

4    Quarters  ^l      1  lard,  u  yd. 

1.  At  4c.  a  nail,  what  will  lyd.  of  ribbon  cost  ? 

2.  At  3c.  an  inch,  what  will  Iqr.  of  a  yard  of  cloth 
cost? 

3.  At  $1  \  a  quarter,  what  will  3  Jyd.  of  cloth  cost  ? 

4.  If   2yd.  3qr.  Ina.  of   cloth  are  required  for  1 
coat,  how  many  yards  are  required  for  4  coats  ? 

5.  What   cost    3yd.  Iqr.  2na.  of  velvet,  at    $2  a 
quarter  ? 

6.  How  many  inches  in  lyd.  3qr.  2na.  lin.  ? 
LONG  MEASURE  is  used  in  measuring  lengths  or 

distances. 

TABLE. 


12 
3 

40* 
8 
3 
60 

8tJO~ 

Inches  (in.) 
Feet 
Yards,  or  16i  Feet 
Rods 
Furlongs 
Miles 
Geographical,  or         1 
•Statute  Allies,  nearly] 
Degrees 

make 

u 
<( 

u 
u 
{( 

1  Foot,                        marl 
1  Yard, 
1  Rod, 
1  Furlong, 
l.Mile. 
1  League, 
J  1  Degree  on  the 
(  Circumference  of  the  Es 
1  Circumference, 

ced      ft. 
yd. 
rd. 
fur. 
m. 

irth,  19. 
circ. 

7.  How  many  rods  in  1  mile  ? 

8.  What  is  the  cost  of  making  40rd.  of  road,  at 
a  rod  ? 

9.  How  many  leagues  in  15  miles  ? 

10.  If  a  ship  sail  20  leagues  a  day,  in  how  many 
days  will  she  sail  300  miles  ? 

11.  In  3  rods  how  many  yards  ?     Feet  ? 

12.  If  a  man  can  travel  4  miles  in  an  hour,  how  long 
will  it  take  him  to  travel  3  leagues  ? 

13.  Hired  a  horse  and  carriage,  at  16§  cents  per 
mile ;  what  did  I  pay  for  a  ride  of  15  miles  ? 

14.  In  33  ft.  how  many  yards  ?     Eods  ? 


Les.  IV.] 


ARITHMETIC. 


97 


LESSON  IV. 
SQUARE  MEASURE  is  used  for  measuring  surfaces. 


TABLE. 


144    Square  Inches  (sq.  in.)  make  1  Square  Foot, 

9    Square  Feet  "      1  Square  Yard, 

30|  Square  Yards,  or  ) 

272J  Square  Feet          j  ^ 

40    Square  Rods  u      1  Rood, 

4    Roods  "      1  Acre, 

G40    Acres 


1  Square  Rod, 


marked  sq.  ft. 
"        sq.  yd. 

"       sq.  rd. 


REMARKS.  1.  A  rectan- 
gle is  a  four-sided  figure, 
which  has  its  corners  or  an- 
gles all  equal  to  each  other, 
as  ABCD,  Fig.  1. 


re  Mile,            "         sq 
FIG.  1. 

m. 
B 

D 


A      FIG.  2. 


2.  A  square  is  a  rectangle  whose 
sides  are  all  equal  to  each  other,  as 
ABCD,  Fig.  2. 

3.  The   small   checks  in  Fig.  1 
are  squares. 


.  Ex.  1.  A  certain  rectangular  garden  is  5  rods  long 
and  3  rods  wide ;  how  many  square  rods  does  it  con- 
tain? See  Fig.  1. 

2.  How  many  rods    round    a  rectangular  garden 
which  is  5  rods  long  and  3  rods  wide  ?     See  Fig.  1. 

3.  How  many  square  rods  in  a  garden  that  is  6 
rods  square  ? 

4.  How  ninny  rods  round  a    square  garden,  each 
side  being  6  rods  long  ? 

5.  How  many  square  rods  in  a  rectangular  garden 
which  is  10  rods  long  and  6  rods  wide  ?     How  many 
rods  round  this  garden  ?     What  will  it  cost  to  fence 
it,  the  fence  costing  $1.25  a  rod  ? 

6.  At  $2  per  square  rod,  what  cost  2  roods  of  land? 

7 


INTELLECTUAL 


[SEC.  V. 


7.  How  many  square  feet  in  a  board  10ft.  long  and 
1ft.  Gin.  wide  ?  12ft.  long  and  2ft.  Sin.  wide  ? 

S.  I  have  a  rectangular  garden,  10  rods  long  and 
containing  50  square  rods  ;  how  wide  is  it  ? 

SOLID  on  CUDIC  MEASURE  is  used  in  measuring 
things  which  have  length,  breadth,  and  thickness. 


172*  Cubic  Inches  (c.  in.) 
27  Cubic  l-'eet 
IS  ("iiliio  1-Vi't 
>  Cunl  1  Yet,  or  ) 
128  Cubic  Feet      J 


TABLE. 

make  1  Cubic  Foot, 
"  1  Cubic  Yard, 
"  1  Cord  Foot, 

"      1  Cord, 


marked  cti.  ft. 
"  c.  yd. 
4  c.  ft. 


REMARKS.  1.     A  cube  is  a 
body,  like    Fig.    3,  which   is 
S      bounded    by    6    equal  square 
~£     faces. 

2.  A  cube  is  also  called 
a  rectangular  prism.  A  rec- 
tangular prism  may  have  its 
length,  breadth,  and  hight  un- 
equal. 

3.  The  volume  or  contents  of  a  cube  or  rectangular 
prism  may  be  found  by  multiplying  the  length  by  the 
breadth,  which  gives  the  area  of  the  top  or  bottom 
face,  and  then  multiplying  this  product  by  the  hight. 

Ex.  9.  How  many  square  feet  are  there  in  the  top 
surface  of  Fig.  3  ? 

10.  How  many  cubic  feet  are  there  in  Fig.  3  ? 

11.  How  many  square  feet  are  there  in  the  6  faces 
of  Fig.  3? 

12.  How  many  cubic  inches  in  a  rectangular  prism 
or  block  which  is  4  inches  long,  3  inches  wide,  and  2 
inches  thick  ?     How  many  square  inches  in  one  of  its 
largest  faces  ?     How  many  in  one  of  its  smallest  faces  ? 
How  many  in  one  of  the  other  faces  ?     How  many  in 
its  G  faces  ? 


LES.  V.]  ARITHMETIC.  99 

13.  How  many  square  feet  in  the  surface  of  a  cubi- 
cal box  whose  edges  are  2  feet  in  length  ? 

14.  How  many  cubic  feet  in  a  cube,  each  edge  of 
which  is  4  feet  long  ? 

15.  How  many  cord  feet  in  48  cubic  feet  of  wood  ? 

1 6.  How  many  cord  feet  in  3  cords  of  wood  ? 

1 7.  What  cost  3  cords  of  wood,  if  4  cord  feet  cost  $3  ? 

18.  How  many  cubic  feet  in  3c.  ft.  8cu.  ft  ? 


LESSON  V. 

LIQUID   MEASURE   is  used   in  measuring   water, 
milk,  beer,  wine,  molasses,  oil,  etc. 

TABLE. 

4  Gills  (gi.)                              make  1  Pint,  marked  pt. 

2  Tints                                           "      1  Quart,  "        qt 

4  Quarts                                        "      1  Gallon,  "      gal. 

1.  At  4c.  a  quart,  what  cost  2gal.  3qt.  of  milk? 

2.  At  25c.  a  pint,  what  will  Igal.  2qt.  Ipt.  of  wine 
cost  ? 

3.  At  60  cents  a  gallon,  what  will  2gal.  2qt.  Ipt.  of 
oil  cost  ? 

4.  What  cost  2gal.  3qt.  Ipt.  of  vinegar,  at  4c.  a 
quart  ? 

5.  What  cost  2qt.  Ipt.  3gi.  of  molasses,  at  2c.  a  gill  ? 

DRY  MEASURE  is  used  in  measuring  grain,  fruit, 
potatoes,  salt,  charcoal,  etc. 

TABLE. 

2  Pints  (pt.)                             make  1  Quart,  marked  ot. 

8  Quarts                                         »      1  pcck,  «      pk. 

4  Peck*                                    f  "      1  Bushel.  «  bush. 

6.  Afc  lOc.  a  quart,  what  costs  1  bu?hel  of  cherries  ? 

7.  At  sL  a  bushel,  what  cost  3pk.  of  corn  ? 

8.  IT  1  bushel  of  chestnuts  costs  $2,  what  will  fiqt. 
cost  ? 

0.  Bought  a  bushel  of  hickory  nuts  for  $1.60  and 
sold  them  at  6Jc.  a  quart ;  how  much  did  I  gain  ? 


100  INTELLECTUAL  [SBO.  V. 

LESSON  VI. 
TIME  is  used  in  measuring  duration. 

TABLE. 

60    Seconds  (sec.)                 make  1  Minute,  marked  m. 

60    Minutes                                  "      1  Hour,  "          h. 

24    Hours                                   "      1  Day,  d. 

7     Days                                    "      1  Week,  "     \vk. 

52    Weeks  and  14  Days,  or  )    u      -,  y  u       w 
3'i.jj  Days                                 ) 

100    Years                                          1  Century,  c. 

The  names  of  the  seasons  and  of  the  months,  and  tho 
number  of  days  in  the  several  months,  are  as  follows  : 

SEASONS.  MONTHS.                       No.  OF  DAYS. 

w.  f          (  1st.  JANUARY,    .......  31 

ter'     )    2d.  FEBRUARY,     ......    28,  in  leap-year  29. 

(  3d.  MARCH,    ........  31 

Spring,      \  4th.  APRIL,    ........    80 

(  5th.  MAY,   .........  31 

(   6th.  JUNE,     ........    30 

Summer,  <   7th.  JULY,       ......        .31 

(  8th.  AUGUST,     .......    31 

(  9th.  SEPTEMBER,     ......  30 

Autumn,   {  10th.  OCTOBER,        ......    31 

tilth.  NOVEMBER,      .    .    .    ...    .30 

Winter,        12th.  DECEMBER,    ......    31 

The  number  of  days  in  each  month  may  be  easily 
remembered  by  committing  the  following  lines 

Thirty  days  hath  September, 
April,  June,  and  November; 
All  the  rest  have  thirty-one 


April,  June,  and  November; 
All  the  rest  have  thirty-one 
Save  the  second  mouth  alone, 


Which  has  just  eight  and  a  score 
Till  leap-year  gives  it  one  more.'* 

1.  How  many  seconds  in  1m.  30sec.? 

2.  How  many  minutes  between  half-past  9  o'clock 
and  noon  ? 

3.  If  a  man  earns  $1  J  per  day,  how  many  dollars 
will  he  earn  in  the  6  working-days  of  a  week  ? 

4.  How  many  days  in  leap  year  from  the  1st  of 
January  to  the  10th  of  March,  inclusive  ?     How  many 
in  a  common  year  ? 

5.  How  many  days  in  June,  July,  and  August  ? 


LES.  I.]  ARITHMETIC.  101 

0.  If  a  boy  can  count  3  in  a  second,  how  many  can 
he  count  in  a  minute  ? 

7.  John  slept  8  hours  each  night ;  how  many  hours 
did  he  sleep  in  a  week  ? 

8.  How  many  hours  in  3  J  days  ?     In  2d.  Gh.  ? 

MISCELLANEOUS  TABLE. 

12  Single  things  make  1  Dozen. 

12  Dozen  u  1  Gross. 

12  Gross  "  1  Great  Gross. 

20  Single  things  "  1  Score. 

5  Score  "  1  Hundred. 

24  Sheets  of  paper  "  1  Quire. 

20  Quires  "  1  Ream. 

250  sheets  of  paper  "  1  Printer's  Token  (small). 

500      "        •'        u  "  1         "  kk       (large). 

56  Pounds  "  1  Bushel  of  corn. 

60  rounds  "  1  Bushel  of  wheat. 

196  Pounds  "  1  Barrel  of  flour. 

200  Pounds  "  1  Barrel  of  beef,  pork,  or  fish. 

0.  At  lOc.  a  dozen,  what  cost  2  gross  of  buttons  ? 
10.  At  3c.  apiece,  what  cost  2  dozen  of  oranges  ? 
1 L.  What  cost  2  reams  of  paper,  at  lOc.  a  quire  ? 
12.  What  cost  2  barrels  of  pork,  at  $8  per  cwt.  ? 


SECTION   SIXTH. 
LESSON  I. 

1.  AT  2  cents  a  yard,  what  will  3  yards  and  ono 
half  of  a  yard  of  braid  cost? 

Solution.  Three  yards  will  cost  3  times  2  cents, 
which  are  G  cents  ;  one  half  of  a  yard  will  cost  ono 
half  of  2  cents,  which  is  1  cent ;  and  1  cent  added 
to  6  cents  makes  7  cents ;  therefore,  etc.  • 

2.  3  times  2  and  one  half  of  2  are  how  many  ? 

3.  At  3  dollars  a  barrel,  what  will  2  barrels  and 
one  third  of  a  barrel  of  apples  cost  ? 

4.  2  times  3  and  one  third  of  3  are  how  many  ? 

5.  At  3  dollars  a  yard,  what  will  4  yards  and  2 
thirds  of  a  yard  of  broadcloth  cost  ? 


102  INTELLECTUAL  [SEC.  VL 

6.  4  times  3  and  2  thirds  of  3  are  how  many  ? 
Solution.  4  timfcs  3  are  12,  and  2  thirds  of  3  are 

2,  which,  added  to  12,  make  14;  therefore,  etc. 

7.  If  a   man   walks  4  miles    per  hour,   how  far 
will  he  walk  in  o  hours  arid  one  fourth  of  an  hour  ? 

8.  3  times  4  and  one  fourth  of  4  are  how  many  ? 

9.  If  a  man  earns  4  shillings  per  day,  how  many 
shillings  will  he  earn  in  5  days  and  3  fourths  of  a  day  ? 

10.  6  times  4  and  3  fourths  of  4  are  how  many  ? 

11.  If  a  man  earns  $5  per  week,  how  many  dol- 
lars will  he  earn  in  4  weeks  and  one  fifth  of  a  week  ? 
How  many  in  6  weeks  and  2  fifths  of  a  week  ? 

12.  4  times  5  and  1  fifth  of  5  are  how  many  ? 

13.  6  times  5  and  2  fifths  of  5  are  how  many  ? 

14.  5  times  5  and  3  fifths  of  5  are  how  many  ? 
15.7  times  5  and  4  fifths  of  5  arc  how  many  ? 

16.  If  wood  is  worth  $6  a  cord,  what  will  3  cords 
and  1  sixth  of  a  cord  cost  ?     What  will  7  cords  and  5 
sixths  of  a  cord  cost  ? 

17.  3  times  6  and  1  sixth  of  6  are  how  many  ? 

18.  7  times  6  and  5  sixths  of  G  are  how  many  ? 

19.  At  $7  a  ton,  what  will  4  tons  and  1  seventh  of  a 
ton  of  coal  cost  ?     What  will  6  tons  and  3  sevenths  of 
a  ton  cost  ? 

20.  4  times  7  and  1  seventh  of  7  are  how  many  ? 

21.  6  times  7  and  3  sevenths  of  7  are  how  many? 

22.  7  times  7  and  5  sevenths  of  7  are  how  many  ? 

23.  At  8  dollars  a  barrel,  what  will  3  barrels  and 
1  eighth  of  a  barrel  of  flour  cost?      What   will    7 
barrels  and  5  eighths  of  a  barrel  cost  ? 

24.  3  times  8  and  1  eighth  of  8  are  how  many  ? 

25.  7  times  8  and  5  eighths  of  8  are  how  many  ? 

26.  4  times  6  and  2  sixths  of  6  are  how  many  ? 

27.  8  times  7  and  2  sevenths  of  7  are  low  many  ? 

28.  4  times  7  and  6  sevenths  of  7  are  how  many  ? 

29.  7  times  8  and  3  eighths  of  8  are  how  many  ? 
oO.  9  times  8  and  7  eighths  of  8  are  how  many  ? 


LES.II.]  ARITHMETIC.  1<  3 

31.  If  a  pound  of  pork  costs  9  cent?,  what  will  3 
pounds  and  1  ninth  of  a  pound  cost?     What  will  5 
pounds  and  4  ninths  of  a  pound  cost  ? 

32.  3  times  9  and  1  ninth  of  9  are  Low  many  ? 

33.  5  times  9  and  4  ninths  of  9  are  hew  numy  ? 

34.  6  times  9  and  7  ninths  of  nine  arc  how  many  ? 

35.  If  a  ton  of  hay  is  worth  $10,  what  are  4.  tons 
and  3  tenths  of  a  ton  worth  ?     What  are  G  tons  and  7 
tenths  of  a  ton  worth  ? 

36.  4  times  10  and  3  tenths  of  10  are  how  many  ? 

37.  6  times  10  and  7  tenths  of  10  rre  how  many  ? 

38.  2  times  10  and  1  tenth  of  10  are  Low  many  ? 

39.  5  times  10  and  9  tenths  of  10  are  how  many  ? 

40.  3  times  10  and  6  tenths  of  10  arc  Low  many  ? 

41.  At  11  dollars  an  acre,  what  will  3  acres  and   L 
eleventh  of  an  acre  of  land  cost  ? 

42.  What  is  meant  by  one  eleventh  of  any  number  ? 
What  by  two  elevenths,  three  eleventh?,  etc.  ? 

43.  3  times  11  and  1  eleventh  of  11  arc  how  many  ? 

44.  6   times  11    and  4   elevenths  of   11  are  how 
many? 

45.  If  a  car  runs  12  miles  per  hour,  how  far  will 
it  run  in  4  hours  and  5  twelfths  of  an  hour  ? 

46.  4  times  12  and  5  twelfths  of  12  arc  how  many  ? 

47.  3  times  12  and  7  twelfths  of  12  arc  Lovr  manv  ? 


LESSON  II. 

REMARK.  Six  shillings  make  a  dollar  in  many  of 
the  United  States,  and  in  this  book  it  will  be  so  un- 
derstood, unless  otherwise  mentioned. 

1.  A  boy  bought  2  pencils,  at  6  cents  npiece ;  how 
many  cents  did  they  cost?     He   paid  for  thorn  with 
peaches,  at  3  cents  apiece ;  how  rnany  peaches  did  it 
take  ? 

2.  2  times  6  are  how  many  times  3  ? 

3.  A  man  bought  4  barrels  of  applet,  at  $•)  u  li-.r- 


104  INTELLECTUAL  [SEC.  VI. 

rel ;  how  many  dollars  did   they  cost  ?     How  much 
wood,  at  $6  a  cord,  would  it  take  to  pay  for  them  ? 

4.  4  times  3  are  how  many  times  6  ? 

5.  Mary  bought  4  oranges,  at  3  cents  apiece  ;  how 
many  cents  did  they  cost  ?     She  paid  for  them  with 
pears,  at  2  cents  apiece  ;  how  many  pears  did  it  take  ? 

6.  4  times  3  are  how  many  times  2  ? 

7.  Bought  5  cords  of  pine  wood,  at  $4  a  cord, 
and  paid  for  it  with  hay,  at  $10  a  ton  ;  how  many  tons 
did  it  take  ? 

8.  5  times  4  are  how  many  times  10  ?          . 

9.  Bought  5  barrels  of  flour,  at  $8  a  barrel,  and 
paid  for  it  with  cloth,  at  $4  a  yard ;  how  many  yards- 
did  it  take  ? 

10.  5  times  8  are  how  many  times  4  ? 

11.  How  much  wool,  at  4  shillings  a  pound,  will 
pay  for  8  bushels  of  corn,  at  6  shillings  a  bushel  ? 

12.  8  times  6  are  how  many  times  4? 

13.  7  times  6  are  how  many  times  3  ? 

14.  6  times  6  are  how  many  times  4? 

15.  How  many  dozen  of  eggs,  at  12  cents  a  dozen, 
will  pay  for  7  pounds  of  veal,  at  6  cents  a  pound  ? 

1 6.  7  times  6  are  how  many  times  12? 

17.  8  times  3  are  how  many  time$4te  ?    4?   5  ?    6  ? 

18.  5  times  7  are  how  many  times  4?    6?   8?   9? 

19.  8  times  5  are  how  many  times  10?   7?    6?    9? 

20.  Bought  3  hundred  weight  and  3  eighths  of  a 
hundred  weight  of  sugar,  at  8  dollars  a  hundred  weight, 
and  paid  for  it  Avith  apples,  at  3  dollars  a  barrel ;  how 
many  barrels  did  it  take  ?     How  much  broadcloth,  at 
4  dollars  a  yard,  would  it  take  to  pay  for  it  ? ' 

21.  3  times  8  and  3  eighths  of  8  are  how  many 
times  3?4?6?5?8?9? 

22.  Sold  4  bushels  and  3  eighths  of  a  bushel  of 
wheat,  at  8  shillings  a  bushel,  and  took  my  pay  in 
butter,  at  2  shillings  a  pound ;  how  many  pounds  did 
I  receive  ? 


LES.  III.]  ARITHMETIC.  105 

23.  4  times  8  and  3  eighths  of  8  are  how  many 

times  2  ?    6  ?    4  ?    7  ? 

24.  How  much  flour,  at  $8  a  barrel,  will  pay  for  5 
boxes  and  5  ninths  of  a  box  of  butter,  at  $9  a  box  ? 

25.  5  times  9  and  5  ninths  of  9  are    how  many 
times  8?    10?    6?    7? 

26.  7  times  10  and  9  tenths  of  10  are  how  many 
(lines  8?    11?    6?    12? 

27.  5  times  7  and  4  sevenths  of  7  are  how  many 
times  12?   8?    6?    5?    9  ? 

28.  9  times  8  and  3  eighths  of  8  are  how  many 
times  5?    10?    12?    7?    11?    3? 

-  29.-  How  many  dollars  will  pay  for  8  bushels  and  4 
sevenths  of  a  bushel  of  wheat,  at  7  shillings  a  bushel  ? 

30.  8  times  7  and  4  sevenths  of  7  are  how  many 
"times  6?  12?  8?  10?  9? 

3L  How  many  bushels  of  corn,  at  one  dollar  a 
bushel,  will  pay  for  9  bushels  and  3  fifths  of  a  bushel 
of  potatoes,  at  5  shillings  a  bushel  ? 

32.  9  times  5  and  3  fifths  of  5  are  how  many  times 
0?  8?  10?  12?  11? 


•*     LESSON  III. 

1 .  IF  2  pears  cost  6  cents,  what  will  4  pears  cost  ? 
Solution.  If  2  pears  cost  6  cents,  1  pear  will  cost  one 

half  of  G  cents,  which  is  3  cents ;  and  4  pears  will  cost 
4  times  3  cents,  which  are  12  cents;   therefore,  etc. 

Or,  since  2  pears  cost  6  cents,  2  times  2  pears,  that 
is,  4  pears,  will  cost  2  times  6  cents,  which  are  12 
cents  ;  therefore,  etc. 

NOTE.  The  first  mode  of  answering  the  above  example  is 
the  more  obvious  analysis  ;  but  the  ready  pupil  will  very  often 
save  labor,  as  in  the  second  solution,  by  a  quick  perception  o^, 
and  a  careful  attention  to,  the  relations  of  numbers. 

2.  4  times  one  half  of  G  are  how  many  ? 

3.  G  times  one  half  of  4  are  how  many  ? 


106  INTELLECTUAL  [SEC.  VL 

4.  If  3  apples  cost  6  cents,  what  will  12  apples  cost  ? 

5.  12  times  one  third  of  6  are  how  many  ? 

6.  6  times  one  third  of  1 2  are  how  many  ? 

7.  A  man  hired  a  laborer,  and  agreed  to  give  him 
§5  for  every  2  days'  work  ;  how  much  did  he  give 
him  for  6  days'  work  ? 

8.  5  times  one  half  of  6  are  how  many  ? 

9.  A  man  lays  up  3  sliillings  a  day ;  in  how  many 
days  will  he  lay  up  $8  ? 

10.  8  times  one  third  of  6  are  how  many? 

11.  If  4  boxes  of  raisins  cost  $7,  what  will  12  boxes 
cost? 

12.  7  times  one  fourth  of  12  are  how  many  ? 

13.  If  3  boxes  of  raisins  cost  $7,  how  many  boxes 
may  be  bought  for  $35  ? 

1 4.  3  times  one  seventh  of  35  are  how  many  ? 

15.  If  7  bushels  of  wheat  are  worth  as  much  as  2 
cords  of  wood,  how  many   bushels  of  wheat  will  pay 
for  10  cords  of  wood? 

16.  7  times  one  half  of  10  are  how  many  ? 

17.  If  10  cords  of  wood  are  worth  as  much  as  35 
bushels  of  wheat,  how  many  bushels  of  wheat  will  pay 
for  2  cords  of  wood  ? 

18.  35  is  how  many  times  one  half  of  10  ? 

19.  How  many  bushels    of  corn,  at  4  shillings  a 
bushel,  will  pay  for  2  barrels  of  apples,  at  3  dollars  a 
barrel  ? 

20.  2  times  3  times  6  are  how  many  times  4  ? 

21.  At  5  shillings  a  gallon,  how  many  gallons  of 
molasses  will  pay  for  2  yards  of  cloth,  at  5  dollars 
a  yard  ? 

22.  2  times  5  times  6  are  how  many  times  5  ?    10  ? 
12?   8? 

23.  How  many  bushels  of  wheat,  at  8  shillings  a 
bushel,  are  worth  as  much  as  4  barrels  of  potatoes,  at 
2  dollars  a  barrel  ? 

24.  4  times  2  times  6  are  how  many  times  8  ?    12  ? 
9?    11? 


LES.  III.]  ARITHMETIC.  107 

25.  A  can  build  12  rods  of  wall  in  4  days,  and  B 
can  build  5  rods  as  often  as  A  builds  3  rods  ;  how 
many  rods  can  B  build  in  4  days  ? 

26.  5  times  one  third  of  12  are  how  many  ? 

27.  A  can  lay  10  rods  of  wall  in  6  days,  and  B  can 
lay  7  rods  as  often  as  A  can  lay  5  rods ;  how  many 
rods  can  B  lay  in  9  days  ? 

28.  7  times  one  fifth  of  10  are  2  thirds  of  what 
number  ? 

29.  A  can  mow  10  acres  of  grass  in  6  days,  but  B 
can  mow  only  4  acres  while  A  is  mowing  5  ;   how 
many  acres  can  B  mow  in  3  days  ? 

.30.  4  times  one  fifth  of  ten  are  2  times  what  num- 
ber ? 

31.  A  boy  bought  20  peaches,  at  the  rate  of  2  for  3 
cents ;  how  many  cents  did  he  pay  for  them  ? 

Solution.  Two  peaches  in  20  peaches  10  times;  and 
10  times  3  cents  are  30  cents ;  therefore,  etc. 

Or,  20  peaches,  at  3  cents  apiece,  cost  60  cents  ; 
but  since  two  peaches  were  bought  for  3  cents,  the  20 
peaches  cost  one  half  of  60  cents',  which  is  30  cents. 

32.  3  times  20  are  how  many  times  2  ? 

33.  How  many  eggs,  at  the  rate  of  3  for  5  cents, 
can  you  buy  for  30  cents  ?    How  many  at  the  rate  of  5 
for  3  cents  ? 

34.  3  times  one  fifth  of  30  are  how  many  ? 

35.  3  times  30  are  how  many  times  5  ? 

36.  5  times  one  third  of  30  are  how  many? 

37.  5  times  30  are  how  many  times  3  ? 

38.  A  hare  has  18  rods  the  start  of  a  hound,  but  th«, 
hound  runs  5  rods  while  the  hare  runs  3  ;  how  many 
rods  must  the  hound  run  to  overtake  the  hare  ? 

Solution.  The  hound  gains  2  rods  by  running  5 
rods  ;  he  must  gain  9  times  2  rods,  and  therefore, 
must  run  9  times  5  rods,  which  are  45  rods. 

39.  5  times  one  half  of  18  are  how  many? 

40.  A  hare  has  24  rods  the  start  of  abound,  but  the 


103  INTELLECTUAL  [SEC.  VI. 

hound  runs  10  rods  while  the  hare  runs  7  ;  how  many 
rods  will  the  hare  run  before  the  hound  overtakes 
him  ? 


LESSON  IV. 

1.  A  BOY  having  12  peaches,  kept  1  third  of  them 
himself,  and  divided  the  other  2  thirds  equally  among 
4  of  his  companions  ;  how  many  did  he  give  them 
apiece  ? 

2.  Two  thirds  of  12  are  how  many  times  4? 

3.  A  boy  having    21    apples,  kept  2   sevenths  of 
them  himself,  and  divided  the  other  5  sevenths  equally 
among  6  of  his  playmates  ;  how  many  did  he  keep  for 
himself  ?     How  many  did  he  give  to  each  of  his  6 
p  lay  mates  ? 

4.  Two  sevenths  of  21  are  how  many? 

5.  Five  sevenths  of  21  are  how  many  times  G? 

6.  A  man  gave  4  fifths  of  30  cents  for  8  oranges  ; 
what  was  the  price  of  1  orange  ? 

7.  Four  fifths  of  30  are  how  many  times  8  ? 

8.  A  man  who  had  $36,  divided  3  fourths  of  his 
money  equally  among  6  poor  persons  ;  how  many  dol- 
lars did  he  give  to  each  ? 

0.  Three  fourths  of  36  are  how  many  times  6  ? 

10.  A  man  bought  a  sheep  for  15  shillings,  and  sold 
it  for  5  thirds  of  what  he  gave  for  it ;  for  how  many 
dollars  did  he  sell  it? 

11.  Five  thirds  of  15  are  how  many  times  6? 

12.  A  boy  bought  a  rabbit  for  25  cents,  and   sold 
him  for  6  fifths  of  his  cost ;  for  how  many  dimes  did  he 
sell  him  ?     How  many  cents  did  the  boy  gain  ?    What 
part  of  a  dime  ? 

13.  Six  fifths  of  25  are  how  many  times  1.0  ? 

14.  A  grocer  having    40  pounds  of  raisins,   sold  5 
eighths  of  them  in  10  equal  parcels ;  how  many  pounds 
were  there  in  each  parcel  ? 


LES.  V.]  ARITHMETIC.  109 

'X  &  4  *»• 

15.  Five  eighths  of  40  are  how  many  times  10  ? 

16.  A  boy  having  48  cents,  paid  away  5  eighths 
of  them  for  oranges  at   3  cents  apiece  ;    how  many 
oranges  did  he  buy  ?     How  many  cents  had  he  left  ? 

17.  Five  eighths  of  48  are  how  many  times  3  ? 

18.  Nine  sevenths  of  28  are  how  many  times  5  ? 
6?   8? 

19.  Seven  fourths  of  36  are  how  many  times  12  ? 
6?   8? 

20.  Five  ninths  of  72  are  how  many  times  10  ?   6  ? 
7?    11? 

21.  .Eleven  eighths  of  64  are  how  many  times  12  ? 
10?   7? 

22.  Three  sevenths  of  84  are  how  many  times  9  ? 
6?   8? 

23.  Five  ninths  of  72  are  how  many  times  7  ?    6  ? 
10? 

24.  Nine  fifths  of  40  are  how  many  times  12  ?    10"  ? 
11? 

25.  Nine  sevenths  of  63  are  how  many  times  10  ? 
8?   7? 

LESSON  V. 

1.  CHARLES   and  Edward  bought  some   oranges : 
Charles  bought  4,  which  was  twice  as  many  as  Ed- 
ward bought ;  how  many  did  Edward  buy  ? 

2.  Four  is  2  times  what  number  ? 

3.  If  2  thirds  of  a  barrel  of  flour  cost    6  dollars, 
what  will  1  third  of  a  barrel  cost  ? 

4.  Six  is  2  times  what  number  ? 

5.  If  3  fourths  of  a  ton  of  coal  cost  6  dollars,  what 
will  1  fourth  of  a  ton  cost  ? 

6.  Six  is  3  times  what  number  ? 

7.  If  2  fifths  of  a  pound  of  butter  cost  8  cents, 
what  will  1  fifth  of  a  pound  cost  ? 

8.  Eight  is  2  times  what  number  ? 


110  INTELLECTUAL  f SEC.  VI. 

9.  If  3  fifths  of  a  pound  of  figs  cost  12  cents,  what 
will  1  fifth  of  a  pound  cost  ? 

10.  Twelve  is  3  times  what  number  ? 

11.  If  4  fifths  of  a  melon  cost  20  cents,  what  will  1 
fifth  of  it  cost  ? 

12.  Twenty  is  4  times  what  number? 

13.  If  5  sixths  of  a  yard  of  calico  cost  15  cents, 
what  will  1  sixth  of  a  yard  cost  ? 

14.  Fifteen  is  5  times  what  number? 

15.  If  it  costs  40  cents  to  lay  4  sevenths  of  a  rod 
of  wall,  what  will  it  cost  to  lay  1  seventh  ? 

1 6.  Forty  is  4  times  what  number  ? 

17.  If  7  eighths  of  a  ton  of  hay  are  worth  $14, 
what  is  1  eighth  of  a  ton  worth  ? 

18.  Fourteen  is  7  times  what  number  ? 

19.  If  3  fourths  of  a  barrel  of  flour  are  worth  $G, 
what  is  1  fourth  of  a  barrel  worth  ?     If  1  fourth  of  a 
barrel  is  worth  $2,  what  is  a  barrel  worth  ? 

20.  If  6  is  3  fourths  of  some  number,  what  is  1 
fourth  of  the  same  number?     Two  is  1  fourth  of  what 
number  ?     Then  6  is  3  fourths  of  what  number? 

21.  If  I  pay  $16  for  4  fifths  of  a  ton  of  hay,  what 
should  I  pay  for  1  fifth  of  a  ton  ?     If  I  pay  $4  for  1 
fifth  of  a  ton,  what  is  the  price  per  ton  ? 

22.  If  16  is  4  fifths  of  some  number,  what  is  1  fifth 
of  the  same  number  ?     Four  is  1  fifth  of  what  number  ? 
Then  16  is  4  fifths  of  what  number  ? 

23.  If  7  eighths  of  an  acre  of  land  are  worth  $21, 
what  is  1  eighth  of  an  acre  worth  ?     If  1  eighth  of  an 
acre  is  worth  $3,  what  is  an  acre  worth  ?    / 

24.  If  21  is  7   eighths  of  some  number,  what  is  1 
eighth  of  the  same  number?     Three  is  1  eighth  of 
what  number  ?    Then  21  is  7  eighths  of  what  number  ? 

25.  If  3  fourths  of  a  pound  of  raisins  cost  15  cents, 
what  will   1  fourth  of  a  pound  cost  ?     What  will  a 
pound  cost  ? 

26.  Fifteen  is  3  fourths  of  what  number  ? 


LB*,VL]  ARITHMETIC.  Ill 

27.  If  5  sevenths  of  a  barrel  offish  cost  10  dollars, 
what  will  1  seventh  of  a  barrel  cost  ?     What  will  a 
barrel  cost  ? 

28.  Ten  is  5  sevenths  of  what  number  ? 

29.  If  5  sixths  of  a  barrel  of  apples  cost  20  shillings, 
how  many  shillings  will  a  barrel  cost  ? 

30.  Twenty  is  5  sixths  of  what  number  ? 

31.  Eighteen  is  6  sevenths  of  what  number? 

32.  Thirty-five  is  5  eighths  of  what  number  ? 

33.  Twelve  is  3  fifths  of  what  number  ? 

34.  Fourteen  is  7  ninths  of  what  number  ? 

35.  Twenty-four  is  6  sevenths  of  what  number  ? 

36.  Sixteen  is  2  fifths  of  what  number? 

37.  Twenty  is  5  ninths  of  what  number  ? 

38.  Twenty-seven  is  9  tenths  of  what  number  ? 

39.  Thirty-two  is  8  ninths  of  what  number  ? 

40.  Fifteen  is  3  sevenths  of  what  number  ? 

41.  Thirty-six  is  6  sevenths  of  what  number? 

42.  Forty  is  10  elevenths  of  what  number? 

43.  Forty-two  is  6  sevenths  of  what  number . 

44.  Forty-eight  is  8  ninths  of  what  number  ? 

45.  Twenty-five  is  5  eighths  of  what  number  ? 

46.  Fifty-six  is  7  ninths  of  what  number  ? 


LESSON  VI. 

1.  IF  3  fourths  of  a  pound  of  raisins  cost  15  cents, 
what  will  a  pound  cost?     How  many  peaches,  at  2 
cents  apiece,  will  it  take  to  pay  for  a  pound  of  raisins  ? 

2.  Fifteen  is  3  fourths  of  how  many  times  2  ? 
Solution.  Since  15  is  3  fourths,  5  is  1  fourth,  and  4 

fourths  will  be  4  times  5,  which  are  20 ;  2  in  20,  10 
times ;  therefore,  15  is  3  fourths  of  10  times  2. 

3.  If  5  eighths  of  a  ton  of  hay  cost  10  dollars, 
what  will  a  ton  cost  ?     How  much  cloth,  at  4  dollars 
a  yard,  will  it  take  to  pay  for  a  ton  of  hay  ? 

4.  Ten  is  5  eighths  of  how  many  times  4  ? 


1 1 2  INTELLECTUAL  [SE.C.  VI. 

5.  A  lady  bought  7  eighths  of  a  yard  of  silk  for  21 
shillings ;  how  many  dollars  would  a  yard  cost,  at  the 
same  rate  ? 

6.  Twenty-one  is  7  eighths  of  how  many  times  6  ? 

7.  A  man  sold  a  cow  for  $32,  which  was  only  8 
ninths  of  what  she  cost  him ;  what  did  she  cost  him  ? 
When  he  bought  her,  .he  paid  for  her  with  wood  at 
$6  a  cord  ;  how  many  cords  did  it  take  ? 

8.  Thirty-two  is  8  ninths  of  how  ^nany  times  6  ? 

9.  Samuel   bought    18   peaches,  which  was  only 
3  eighths  as  many  as  Henry  bought ;  how  many  did 
Henry  buy  ?     Henry  paid  for  his  peaches  with  mel- 
ons, giving  1  melon  for  12  peaches;  how  many  melons 
did  it  take? 

10.  Eighteen  is  3  eighths  of  how  many  times  12  ? 

11.  A  man   being  asked  the  age  of  his  youngest 
son,  replied  that  the  age  of  his  oldest  son  was   18 
years,  which  was  just  3  eighths  of  his  own  age,  and 
that  his  own  age  was  1 6  times  the  age  of  his  youngest 
son  ;  what  was  the  father's  age  ?     What  was  the  age 
of  his  youngest  son  ? 

12.  Eighteen  is  3  eighths  of  how  many  times  16  ? 

13.  Twenty-four  is  3  fifths  of  how  many  times  4  ? 

14.  Thirty  is  5  sixths  of  how  many  times  5  ? 

15.  Thirty-two  is  8  elevenths  of  how  many  times  6  ? 

16.  Thirty-five  is  7  ninths  of  how  many  times  10  ? 

17.  Thirty-six  is  4  sevenths  of  how  many  times  8  ? 

18.  Forty  is  5  sevenths  of  how  many  times  9  ?     . 

19.  Forty-two  is  6  sevenths  of  how  many  times  4  ? 

20.  Forty-five  is  9  twelfths  of  how  many /times  6  ? 

21.  Forty-eight  is  6  ninths  of  how  many  times  12  ? 

22.  Fifty  is  5  sixths  of  how  many  times  8  ? 

23.  Forty-nine  is  7  eighths  of  how  many  times  10  ?  - 

24.  Sixty  is  5  sevenths  of  how  many  times  8  ? 

25.  Sixty-three  is  7  eigKths  of  how  many  times  12? 

26.  Sixty-four  is  8  ninths  of  how  many  times  6  ? 

.  27.  Sixty-five  is  5  sixths  of  how  many  times  10  ? 


, 
LES.  VII.]  ARITHMETIC.  113 

28.  Seventy  is  10  sevenths  of  how  many  times  8  ? 

29.  Seventy-two  is  12  fifths  of  how  many  times  4? 

30.  Seventy-five  is  5  fourths  of  how  many  times  9  ? 

31.  Eighty  is  10  sevenths  of  how  many  times  6  ? 

32.  Eighty  is  8  thirds  of  how  many  times  8  ? 

LESSON  VII , 

1.  A   BOY   gave  away  2    apples,  which  was    one 
third  of  all  he  had ;  how  many  had  he  at  first  ?    How 
many  did  he  keep  ? 

2.  Sarah  is  5  years  old,  and  she  is  one  fourth,  as 
old  as  her  brother ;  how  old  is  her  brother  ?     How 
much  older  is  he  than  Sarah  ? 

3.  A  boy  gave  away  10  cents,  which  was  2  thirds 
of  all  the  money  he  had ;  how  many  cents  had  he  ? 

4.  A  boy  soid  a  dove  for  15  cents,  which  was  3 
fourths  of  what  it  cost  him ;  how  much  did  he  lose  by 
the  bargains  ? 

5.  If  15  is  3  fourths  of  some  number,  what  is  1 
fourth  of  the  same  number  ? 

6.  A  man  paid  away  $12,  which  was  3  fifths  of 
all  the  money  he  had ;  how  many  dollars  did  he  keep  ? 

7.  If  12  is  3  fifths  of  some  number,  what  is  2  fifths 
of  the  same  number.  ? 

8.  A  man  sold  a  watch  for  $24,  which  was  only  3 
fifths  of  what  it  cost  him  ;  what  did  it  cost  him  ? 

9.  Twenty-four  is  3  fifths  of  what  number  ? 

10.  A  man  sold  a  horse  for  $30,  which  was  only  5 
sevenths  of  what  he  paid  for  him ;  how  much  did  he 
lose  by  his  bargains  ? 

11.  If  30  is  5  sevenths  of  some  number,  what  is  2 
sevenths  of  the  same  number  ?     Thirty  is  5  sevenths 
'of -what  number  ? 

12.  A  man  sold  3  watches  for  $36,  which  was   6 
fifths  of  what  they  cost  him ;  what  did  they  cost  him 
apiece  ? 

8 


1  -  -1         .  INTELLECTUAL  [SEO.  VI. 

13.  Thirty-six  is  6  fifths  of  how  many  times  3  ? 

14.  There  is  a  pole  standing  so  that  1  third  of  it  is 
under  wilt  e  i1,  and  8  feet  above  water;  what  part  of  the 
pole  is  above  water  ?     How  long  is  the  pole  ? 

lo.  There  is  a  pole  standing  so  that  2  thirds  of  it 
are  under  water,  and  5  feet  out ;  how  long  is  the  pole  ? 

1 0.  There  is  a  pole  3  iifths  under  water,  and  8  feet 
out;  what  part  of  the  pole  is -above  water  ?  How  long 
is  the  pole  ? 

17.  There  is  a  pole  standing  so  that  2  sevenths  of 
it  are  in  the  mud,  3  sevenths  in  the  water,  and  6  feet 
above  water  ?     What  part  of  the  pole  is  above  water  ? 
How  long  i.->  the  pole?     How  many  feet  are  in  the 
mud?     How  many  in  the  water? 

18.  There  is  an  orchard  in  which  5  ninths  of  the 
trees  bear  apples,  2  ninths  bear  peaches,  1  ninth  bear 
pears,  and  G  trees  bear  cherries  ;  how  many  trees  are 
there  in  the  orchard  ?     How  many  of  each  kind  ? 

39.  Three  sevenths  of  the  trees  in  a  certain  orchard 
bear  cherries,  2  sevenths  bear  peaches,  10  trees  bear 
pears,  and  G  bear  plums  ;  how  many  trees  are  there  in 
the  orchard  ?  How  many  of  each  kind  ? 

2  ).  In  a  eorUsn  school  3  ninths  of  the  pupils  study 
.arithmetic,  2  ninths  study  grammar,  1  ninth  study 
history,  1  ninth  study  algebra,  and  8  pupils  study 
geometry;  how  many  pupils  are  there  in  the  school? 
How  many  attending  to  each  study? 

21.  There  i-  a  school  in  which  3  elevenths  of  the 
scholar  3  stiirly  Latin,  2  elevenths,  study  Greek,  4  elev- 
en tin  study  arithmetic,  9    scholars  study  Algebra,  and 
7  study  <i  corn ''try  ;  how  many  scholars  are  there  in 
t'ie  school  ?     How  many  attending  to  each  study  ? 

22.  A  man  sold  a  cow  for  $35,  which  was  7  fifths 
of  what  she  co  t  him;  how  much  did  he  gain  by  the 
bargain.-  ? 

2  ].  If  35  is  7  fifths  of  some  number,  what  is  2  fifths 
01"  the  same  number  ? 


LES.  VIII]  ARITHMETIC.  1 1 5 

LESSON  VIII. 

1.  Two  boys  were  counting  their  money,  when  one 
said  he  had  6  cents.    Well,  said  the  other,  2  thirds  of  " 
your  money  is  exactly  1  fifth  of  mine  ;  now,  if  you 
will  tell  me  how  many  cents  I  have,  I  will  give  you 
one  half  of  them.     How  many  cents  had  he  ? 

2.  Two  thirds  of  6  ar.e  1  fifth  of  what  number  ? 

3.  A  boy  being  asked  how  many  chickens  he  had, 
said  that  he  had  them  in  two  coops  :  in  one  coop  he 
had  12,  and  3  fourths  of  these  were  just  1  fifth  of 
what  he  had  in  the  other  ;  required  the  number  in 
the  other  coop  ?• 

4.  Three  fourths  of  1 2  are  1  fifth  of  what  number  ? 

5.  Two  boys  were  talking  of  their  ages,  when  one 
of  them  said  he  was  twelve  years  old.     Well,  said  the 
other,  2  thirds  of  your  age  are  exactly  4  fifths  of  mine ; 
and  if  you  will  tell  me  how  old  I  am,  I  will  give  you 
as  many  apples  as  I  am  years  old.  What  was  his  age  ? 

G.  Two  thirds  of  12  are  4  fifths  of  what  number? 

7.  A  man  being  asked  the  age  of  his  oldest  son, 
replied  that  his  youngest  son  was  8  years  old,  and 
that  3  fourths  of  the  youngest  son's  age  were  just  2 
sevenths  of  the  age  of  his  oldest  son  ;  how  old  was  the 
oldest  son  ? 

8.  Three  fourths  of  8  are  2  sevenths  of  what  number  ? 

9.  A  man  being  asked  how  many  sheep  he  had, 
said  that  he  had  them  in  two  pastures  ;  in  one  he  had 
32,  and  5  eighths  of  these  were  2  ninths  of  what  he 
had  in  the  other  pasture  ;  how  many  had  he  in  the 
other  ? 

10.  5  eighths  of  32  are  2  ninths  of  what  number  ? 

11.  3  fifths  of  10  are  2  sevenths  of  what  number  ? 

12.  4  sevenths  of  21  are  3  eighths  of  what  number  ? 

13.  5  sixths  of  24  are  4  ninths  of  what  number  ? 

14.  5  thirds  of  24  are  4  sevenths  of  what  number? 

15.  8  sevenths  of  21  are  4  fifths  of  what  number? 


1 1 6  INTELLECTUAL  [SEC.  VI. 

1 G.  Charles  is  35  months  old,  and  4  fifths  of  his  age 
are  7  sixths  of  Mary's  age ;  how  many  years  old  is  Mary  ? 

17.  4  fifths  of  35  are  7  sixths  of  how  many  times  12  ? 

18.  4  fifths  of   25  are  10  sevenths  of  how  many 
times  5  ? 

Solution.  1  fifth  of  25  is  5,  and  4  fifths  are  4  times 
5,  which  are  20 ;  if  20  is  10  sevenths,  1  seventh  is  1 
tenth  of  20,  which  is  2,  and  7  sevenths  are  7  times  2, 
which  are  14 ;  5  in  14,  2  times  and  4  fifths  :  therefore 
4  fifths  of  25  are  10  sevenths  of  2  times  5  and  4  fifths 
of  5. 

19.  4  sevenths  of  28  are  2   fifths    of  how   many 
times,  9  ? 

20.  *3  fifths  of  30  are  9  tenths  of  how  many  times  8  ? 

21.  3  eighths  of  32  are  6  sevenths  of  how  many 
times  9  ? 

22.  6  ninths  of  3G  are  8  fifths  of  how  many  times  4  ? 

23.  3  fifths  of  40  are   6  elevenths  of  how  many 
times  7  ? 

24.  8  ninths  of  45  are  10  sixths  of  how  many  times 
3? 

25.  5  eighths  of  48  are  3  fourths  of  how  many  times 
12? 

26.  3  eighths  of  64  are  4  ninths  of  how  many  times 
10? 

27.  5  ninths  of  72  are  4  fifths  of  how  many  times  6  ? 

LESSON  IX. 

1.  FOUR  sevenths  of  42  are  8  ninths  of /how  many 
fifths  of  35  ? 

Solution.  1  seventh  of  42  is  G,  and  4  sevenths  are  4 
times  G,  which  are  24  ;  if  24  is  8  ninths,  1  ninth  is  1 
eighth  of  24,  which  is  3,  and  9  ninths  are  9  times  3, 
which  are  27  ;  1  fifth  of  35  is  7,  and  7  in  27,  3  timos 
and  6  sevenths  of  a  time  ;  therefore,  4  sevenths  of  42 
are  8  ninths  of  3  fifths  and  6  sevenths  of  a  fifth  of  35. 


LES.  X.]  ARITHMETIC.  117 

2.  3    fifths  of  20    are    6    sevenths    of  how  many 
eighths  of  24  ? 

3.  3  sevenths  of  28  are  4  fifths  of  how  many  ninths 
of  18? 

4.  3  eighths  of  32  are  6  tenths  of  how  many  sixths 
of  42  ? 

5.  4   ninths  of  81  are  6    sevenths    of  how  many 
thirds  of  24  ? 

6.-  2  eighths  of  72  are  6  fifths  of  how  many  ninths 
of  36? 

7.  5  eighths  of  56  are  5  ninths  of  how  many  tenths 
of  100? 

8.  3  eighths  of  64  are  6  sevenths  of  how  many  sev- 
enths of  35  ? 

9.  9  sevenths  of  28  are  3  fifths  of  how  many  sixths 
of  48? 

10.  3    tenths  of  100    are    5    ninths    of  how  many 
fourths  of  32  ? 

11.  5  eighths  of  32  are  10  sixths  of  how  many  fifths 
of  20? 

12.  3  fourths  of  48  are   6  sevenths  of  how  many 
thirds  of  24  ? 


LESSON  X. 

1.  IF  1  barrel  of  flour  costs  $6,  what  will  4  bar- 
rels cost  ? 

2.  If  2  barrels  of  apples  are  worth  $6,  what  are  8 
barrels  worth  ? 

3.  What  will  3  yards  of  cloth  cost,  if  8  yards  cost 
$:>2  ? 

4.  Two  couriers,  A  and  B,  are  21  miles  apart,  and 
traveling  in  the  same  direction.     A,  who  is  before  B, 
travels  5  miles,  and  B  travels  8  miles  an  hour ;  in  how 
many  hours  will  B  overtake  A  ?     How  many  miles 
will  A  go  before  B  overtakes  him?     How  far  must 
B  go  to  overtake  A  ? 


118  INTELLECTUAL  [SEC.  VI. 

5.  Two  couriers,  12  miles  apart,  are  traveling  in 
the  same  direction ;  but  the  foremost  goes  only  3  miles 
while  the  other  goes  5  miles  ;  how  far  will  each  go 
before  they  will  be  together  ? 

G.  A  and  B  are  60  miles  apart,  and  traveling 
towards  each  other ;  while  A  goes  4  miles,  B  goes  G  ; 
how  many  miles  will  each  travel  before  they  meet  ? 

7.  A  boy  having  25  apples,  kept  4  himself,  and 
divided  the  rest  equally  among  3  companions  ;  how 
many  did  he  give  them  apiece  ? 

S.  How  many  chairs,  at  $3  each,  may  be  bought 
for  $36  ? 

9.  How  many  sheep,  at  $8  each,  may  be  bought 
for  $48  ? 

10.  How  many  tables,  at  $9  each,  may  be  bought 
for  $G3  ? 

1 1.  A  man  bought  3  barrels  of  flour,  at  $7  a  barrel, 
5  yards 'of  cloth,  at  $4  a  yard,  and  1  ton  of  coal  for 
$9  ;  what  did  he  pay  for  all  ? 

1  "2.  If  4  tons  of  hay  will  keep  2  cows  through  the 
winter,  how  many  tons  will  keep  12  cows  the  same 
time? 

13.  If  a  man  spends  8  shillings  a  day,  how  many 
dollars  will  he  spend  in  6.  days  ?     In  9  days  ? 

14.  If  a  man  ear  as   $00  in   12  weeks,  how  much 
does  he  earn  in  1  month,  or  4  weeks  ?     How  much 
in  3  weeks  ?     In  5  weeks  ? 

15.  Bought  5  pieces  of  cloth,  each  containing  10 
yards,  for  $100  ;   what  was  the  cost  of  each  piece  ? 
'What  the  price  per  yard  ? 

1 6.  If  2  men  spend  $24  in  3  weeks,  how  many  dol- 
lar-, at  the  same  rate,  will  5  men  spend  in  4  weeks  ? 

17.  If  4  horses  eat  12  bushels  of  oats  in  3  weeks, 
how  many  horses   will  eat  24  bushels  in  the  same 
time? 

18.  If  2  horses  eat  4  bushels  of  oats  in  8  days,  how 
many  bushels  will  3  horses  eat  in  1 2  days  ? 


LES.  X.]  ARITHMETIC.  1 1  '.* 

19.  If  6  horses  eat  9  bushels  of  oats  in  5  (lays,  in 
how  many  days  will  3  horses  eat  18  bushels  ? 

20.  A  ship's  crew  of  9  men  have  provisions  for  2 
months  ;  how  many  months  will  the  same  provisions 
last  6  men  ? 

21.  A  ship  has  food  for  2  men  for  12  months  ;  how 
many  men  will  it  last  4  months  ? 

22.  If  a  staff  3  feet  long  casts  a  shadow  4  fret  at  0 
o'clock,  what  is  the  length  of  a  pole  that  casts  a  shadow 
20  feet,  at  the  same  time  ? 

23.  If  a  staff  3  feet  long  casts  a  shadow  2  feet  at 
12  o'clock,  what  is  the  length  of  the  shadow  cast,  at 
the  same  time,  by  a  pole  18  feet  long? 

24.  If  4 'men  can  do  a  piece  of  work  in  6  days,  in 
how  many  days  can.  3  men  do  the  same  ? 

25.  If  5  men  can  do  a  piece  of  work  in  3  day-, 
in   how  many  days  can  they  do  a  piece  of  work  5 
times  as  large  ? 

26.  If  36  men  can  do  a  piece  of  work  in  4  days, 
how  many  men   can   do  twice  as   much  work  in  2 
days  ? 

27.  A  man  bought  3  barrels  of  flour  for  21  dol- 
lars ;  at  what  price  per  barrel  must  he  sell  it  to  gain 
6  dollars  on  the  lot  ? 

28.  A  man  bought  5  barrels  of  flour,  at  $fi  a  bar- 
rel ;  for  what  sum  must  the  whole  lot  be  sold  to  gain 
$10? 

29.  A  man  bought  5  casks  of  nails,  at  7  dollars  a 
cask;  at  what  price  per  cask  must  he  sell  them  to 
gain  15  dollars  ? 

30.  A  man  bought  6  yards  of  cloth  for  24  dollars. 
and  sold  it  at  6  dollars  a  yard ;  how  much  did   he 
gain  by  the  bargains  ? 

31.  A  boy  bought  8  oranges^  at  3  cents  apiece,  an.d 
sold  them  all  for  40  cents  ;  how  much  di  1  he  gain  ;  >y 
the  bargains  ? 

32.  A  man  bought  a  lot  of  hay,  at  £•'  2  fi  ion,  atitl 


120  INTELLECTUAL  [SEC.  VI. 

sold  it  at  $14  a  ton,  by  which  he  gained  $16  ;  how 
many  tons  did  he  buy  ? 

33.  By  buying  cloth  at  $4  a  yard,  and  selling  it  at 
$3  a  yard,  I  lost  $6  ;  what  did  I  pay  for  all  of  the 
cloth  ? 

34.  A  cabinet-maker  exchanged  3  bureaus,  worth 
$8  apiece,  for  chairs  worth  $2    apiece  ;   how  many 
chairs  did  he  receive  ? 

35.  B  can  build  5  rods  of  wall  while  A  builds  4  ; 
how  many  rods  can  B  build  while  A  is  building  24 
rods? 

LESSON  XI. 

1.  AT  7  dollars  a  barrel,  what  will  3  barrels  and 
1  half  of  a  barrel  of  flour  cost  ? 

2.  3  times  7  and  1  half  of  7  are  how  many  ? 

3.  If  coal  is  worth  $9  a  ton,  what  shall  I  pay  for 
4  tons  and  1  fourth  of  a.  ton  ?     What  for  5  tons  and  3 
fourths  of  a  ton  ? 

4.  5  times  9  and  3  fourths  of  9  are  how  many  ? 

5.  Bought  5  yards  and  3  eighths  of  a  yard  of  vel- 
vet, at  $8  a  yard,  and  paid  for  it  .with  broadcloth,  at 
$4  a  yard ;   how  many  yards    of  broadcloth   did  it 
take? 

6.  5  times   8  and  3    eighths  of  8  are  how  many 
times  4? 

7.  Bought  3  tons  and  5  eighths  of  a  ton  of  hay,  at 
$16  a  ton,  and  paid  for  it  with  flour,  at  $8  a  barrel  ; 
how   many  barrels  did  it  take  ? 

8.  3  times  16  and  5  eighths  of  16  are  Jiow  many 
times  8  ? 

9.  5  times  12  and  5  sixths  of  12  are  how  many 
times  8  ?   9  ?    6  ?   5  ? 

10.  7    times  10  and  3  fifths  of  10  are   how  many 
times  12?   9  ?    11?   8? 

11.  6  tunes  9   and   2   thirds  of  9   are   how  many 
times  6?    10?   8?    12?   7? 


LES.  XI.J  ARITHMETIC.  '1-1 

12.  If  6  barrels  of  apples  cost  $18,  what  part  of 
$18   will   1    barrel  cost?     What  part  of  $18  will  2 
barrels  cost  ?    3  barrels  ?    4  barrels  ?    5  barrels  ? 

13.  What  is  1  sixth  of  18  ?    1  third  of  18  ?    1  half 
of  18  ?    2  thirds  of  18  ?    5  sixths  of  18  ? 

14.  If  8  yards  of  cloth  cost  $24,  what  part  of  $24 
will  1  yard  cost  ?    2  yards  ?    3  yards  ?    4  yards  ?   5 
yards  ?    6  yards  ?    7  yards  ? 

15.  What  is  1   eighth  of  24  ?    1  fourth  of  24?   3 
eighths  of  24  ?     1  half  of  24  ?     5  eighths  of  24  ?     3 
iburths  of  24  ?    7  eighths  of  24  ? 

16.  If  12  cords  of  wood  cost  $48,  what  part  of  $48 
will  1  cord  cost  ?     2  cords  ?     3  cords  ?    4  cords  ?    5 
cords  ?    6  cords  ?    7  cords  ?    8  cords  ?    9  cords  ?    10 
cords  ?    11  cords  ? 

*7.  What  is  1  twelfth  of  48  ?  1  sixth  of  48  ?  1 
fourth  of  48  ?  1  third  of  48  ?  5  twelfths  of  48  ?  1 
half  of  48  ?  7  twelfths  of  48  ?  2  thirds  of  48  ?  3 
fourths  of  48  ?  5  sixths  of  48  ?  11  twelfths  of  48  ? 

18.  A  boy  having  28  cents,  gave  5  sevenths  of  them 
for  peaches,  at  2  cents  apiece  ;  how  many  peaches  did 
he  buy  ? 

19.  5  sevenths  of  28  are  how  many  times  2  ?    5  ? 

20.  A  man  bought  a  sheep  for  21  shillings,  and  sold 
it  for  8  sevenths  of  what  he  paid  for  it ;  how  many 
dollars  did  he  receive  for  the  sheep  ? 

21.  8  sevenths  of  21  are  how  many  times  6?   3? 
12?.   8?    4? 

22.  Six  men,  setting  out  on  a  journey,  took  5  loaves 
of  bread  apiece;   but  before  they  had  eaten  any  of  it 

•  -i:  other  men  joined  them,  and  the  bread  was  divided 
equally  among  the  whole  company.  How  many  loaves 
di  1  each  man  have  ? 

2-3.  Six  times  5  are  how  many  times  10  ?   8  ?    4  ?   3  ? 

24.  A  man  had  24  cords  of  wood,  and  sold  3  eighths 
of  it  for  $54;  what  was  the  price  per  cord? 

25.  54  are  how  many  times  3  eighths  of  24  ? 


122  INTELLECTUAL  [SEC.  VI. 

26.  A  man  had  36  sheep,  and  sold  5  ninths  of  them 
at  4  dollars  a  head  ;  how  many  dollars  did  he  receive  ? 

27.  How  many  are  4  times  5  ninths  of  36  ? 

28.  If  5  eighths  of  a  box  of  raisins  cost  15  shillings, 
how  many  bushels  of  oats,  at  4  shillings  a  bushel,  will 
pay  for  a  box  of  raisins  ? 

29.  8  fifths  of  fifteen  are  how  many  times  4  ?    6  ? 

30.  A  man  gave  25  cents  for  his  breakfast,  which 
was  5  eighths  of  what  he  gave  for  his  dinner  ;  what  did 
he  give  for  his  dinner  ? 

31.  A  man  paid  45  cents  for  his  dinner,  which  was 
9  sevenths  of  what  he  paid  for  his  breakfast;  what 
did  his  breakfast  cost  ? 

32.  A  teacher,  when  asked  how  many  pupils  he  had, 
replied  that  they  were  in  2  rooms  :  in  one  room  there 
were  32,  and  5  eighths  of  these  were  2  fifths  of  the 
number  in  the  other ;  how  many  pupils  were  there  in 
the  other  room  ?     How  many  in  both  ? 

~~  33.  5  eighths  of  32  are  2  fifths  of  what  number  ? 

34.  A  boy  being  asked  how  old  his  dog  was,  said 
that  his  cat  was  8  years  old,  that  the  age  of  his  cat  was 
4  thirds  of  the  age  of  his  rabbit,  and  that  his  dog  was 
twice  as  old  as  his  rabbit ;  how  old  was  his  dog  ? 

LESSON  XII. 

1.  How  many  are  2  times  13  ?  13  times  2  ? 

2.  How  many  are  2  times  14?  14  times  2? 

3.  How  many  are  2  times  15?  15  times  2? 

4.  How  many  are  2  times  16?  16  times  2  ? 

5.  How  many  are  2  times  17  ?  17  times  2  ? 

6.  How  many  are  2  times  18  ?  18  times  2  ? 

7.  How  many  are  2  times  19  ?  19  times  2  ? 

8.  How  many  are  2  times  20  ?  20  times  2  ? 

9.  How  many  are  2  times  21  ?  21  times  2  ? 

10.  How  many  are  2  times  22?         22  times  2? 

11.  How  many  are  2  times  23?         23  times  2? 


LBS.  XII.] 


ARITHMETIC. 


123 


12.  How  many  are  2  times  24? 

24  times  2  ? 

13.  How  many  are  2  times  25  ? 

25  times  2  ? 

14.  How  many  are  3  times  13  ? 

13  times  3? 

15.  How  many  are  3  times  14? 

14  times  3? 

16.  How  many  are  3  times  15  ? 

15  times  3  ? 

17.  How  many  are  3  times  16? 

16  times  3? 

18.  How  many  are  3  times  17  ? 

17  times  3  ? 

19.  How  many  are  3  times  18? 

18  times  3? 

20.  .Plow  many  are  3  times  19? 

19  times  3? 

21.  How  many  are  3  times  20? 

20  times  3  ? 

22.  How  many  are  3  times  21  ? 

21  times  3? 

23.  How  many  are  3  times  22  ? 

22  times  3  ? 

24.  How  many  are  3  times  23  ? 

23  times  3  ? 

25.  How  many  are  3  times  24  ? 

24  times  3  ? 

26.  How  many  are  3  times  25  ? 

25  times  3  ? 

27.  How  many  are  4  times  13? 

13  times  4? 

28.  How  many  are  4  times  14? 

14  times  4? 

29.  How  many  are  4  times  15? 

15  times  4  ? 

30.  How  many  are  4  times  16? 

16  times  4? 

31.  How  many  are  4  times  17? 

17  times  4? 

32.  How  many  are  4  times  18? 

18  times  4? 

33.  How  many  are  4  times  19? 

19  times  4? 

34.  How  many  are  4  times  20  ? 

20  times  4  ? 

35.  How  many  are  4  times  21  ? 

21  times  4? 

36.  How  many  are  4  times  22  ? 

22  times  4  ? 

37.  How  many  are  4  times  23  ? 

23  times  4  ? 

38.  How  many  are  4  times  24? 

24  times  4  ? 

39.  How  many  are  4  times  25  ? 

25  times  4  ? 

40.  How  many  are  5  times  13? 

13  times  5  ? 

41.  How  many  are  5  times  14? 

1  4  times  5  ? 

42.  How  many  are  5  times  15? 

15  times  5? 

43.  How  many  are  5  times  16? 

1  6  times  5  ? 

44.  How  many  are  5  times  17? 

17  times  5? 

45.  How  many  are  5  times  18? 

18  times  5? 

46.  How  many  are  5  times  19? 

19  times  5? 

47.  How  many  are  5  times  20  ? 

20  times  5  ? 

48.  How  many  are  5  times  21? 

2  1  times  5  ? 

124  INTELLECTUAL  [SEC.  TI 

49.  How  many  are  5  times  22  ?         22  times  5  ? 

50.  How  many  are  5  times  23  ?         23  times  5  ? 

51.  How  many  are  5  times  24?         24  times  5  ? 

52.  How  many  are  5  times  25  ?         25  times  5  ? 

53.  How  many  are  6  times  13?         13  times  6? 

54.  How  many  are  6  times  14?         14  times  G? 

55.  How  many  are  6  times  15?         15  times  6? 

56.  How  many  are  6  times  16?         16  times  6? 

57.  How  many  are  6  times  17?         17  times  6? 

58.  Plow  many  are  6  times  18?         18  times  6? 

59.  How  many  are  6  times  19  ?         19  times  6? 

60.  How  many  are  6  times  20  ?         20  times  6  ? 

61.  How  many  are  6  times  21  ?         21  times  6? 

62.  How  many  are  6  times  22  ?         22  times  6  ? 

63.  How  many  are  6  times  23  ?         23  times  6  ? 

64.  How  many  are  6  times  24?         24  times  6? 

65.  How  many  are  6  times  25  ?         25  times  6  ? 

66.  Count  by  6's  to  96;   thus,  6,  12,  18,  etc. 

67.  Count  backward  by  6's;  thus,  96,  90,  84,  etc. 

68.  Count  by  6's  from  3  to  99  ;  thus,  3,  9,  15,  etc. 

69.  Count  backward  by  6's ;  thus,  99,  93,  87,  etc. 

70.  Count  by  7's  to  98  ;  thus,  7,  14,  21,  etc. 

71.  Count  backward  by  7's  ;  thus,  98,  91,  84,  etc. 

NOTE.  Such  exercises  as  the  last  six  examples  above  should 
be  continued  only  a  very  few  minutes  at  a  time.  Let  the  ex- 
ercise be  varied  by  allowing  the  class  to  recite  sometimes  in 
concert,  sometimes  individually ;  by  allowing  one  pupil  to  name 
one  number,  and  another  the  next ;  by  letting  two  or  more  pu- 
pils recite  simultaneously,  one  counting  from  one  number,  and 
another  from  another  number ;  or  by  any  other  mode  which 
shall  secure  the  attention  and  awaken 'the  interest  pf  the  class. 

The  more  complicated  of  the  above  plans,  if  adopted,  should 
be  commenced  with  the  2's,  the  5's,  the  10's,  and  other  numbers 
which  give  the  more  simple  combinations  ;  and  they  should  not 
be  continued  unless  the  pupils  have  the  ability  to  proceed  with- 
out confusing  each  other. 

These  exercises,  if  judiciously  conducted,  are  very  valuable ; 
and  when  the  pupil  shall  have  acquired  the  ability  to  make  all 
such  combinations  with  accuracy  and  rapidity,  he  will  have  very 
great  facility  in  all  the  processes  of  addition  and  subtraction. 


LES,  L]  ARITHMETIC.  125 

SECTION  SEVENTH. 
LESSON  I. 

1.  A  MERCHANT  sold  5  yards  of  cloth,  at  J  of  a  dol- 
lar per  yard  ;  what  did  he  receive  for  it  ? 

2.  What  is  5  times  J  ?     Ans.  %  X  5  =  £  ='!§. 

3.  How  many  are  f  X  3  ?    f  X  5  ? 

4.  How  many  are  f  X  4  ?    $  X  7  ? 

5.  How  many  are  3  times  $  ? 
-4ws.  Three  times  f  are  f ,  or  §. 

NOTE.  The  |.  are  obtained  by  multiplying  the  numerator 
by  3,  and  the  J.  are  obtained  by  dividing  the  denominator  by  3. 
In  examples  like  this,  it  is  better  to  divide  the  denominator, 
because  it  gives  the  answer  in  smaller  or  lower  terms. 

6.  How  many  are  5  times  -^  ?     "Why  ? 

7.  At  -1*5  of  a  dollar  a  pound,  what  will  5  pounds 
of  butter  cost  ? 

Solution.  Five  pounds  will  cost  5  times  as  much  as  1 
pound ;  5  times  ^  of  a  dollar  are  f  of  a  dollar  =  $1-J, . 

8.  At  f  of  a  dollar  per  pound,  what  will  4  pounds 
of  butter  cost  ? 

9.  What  will  6  yards  of  silk  cost,  at  ||  of  a  dollar 
per  yard  ? 

10.  If  1  horse  eats  ^T  of  a  ton  .of  hay  in  a  month, 
how  much  will  7  horses  eat  in  the  same  time  ? 

11.  If  1  man  can  reap  ^J  of  an  acre  of  rye  in  a  day, 
how  much  can  8  men  reap  in  the  same  time  ? 

12.  If  1  yard  of  cloth  costs  |f  of  a  dollar,  what  will 
8  yards  cost  ? 

13.  How  many  are  8  times  |f  ?   9  times  -J-J? 

14.  How  many  are  6  times  ff  ?    11  times  Jf  ? 

15.  How  many  are  5  times  f  ? 
Ans.  Five  times  f  are  f ,  or  3. 

NOTE.  The  pupil  will  observe  that  if  a  fraction  is  multiplied 
by  its  denominator,  the  product  is  the  numerator. 

16.  How  many  are  11  times  -^T  ?     Why  ? 


126  INTELLECTUAL  [SEC..  VII. 


17.  How  many  are  9  times  f  ?    15  times 

18.  How  many  are  23  times  JJ  ?    49  times 

19.  What  cost  8  boxes  of  strawberries,  at  f  of  a 
dollar  per  box  ? 

20.  What  cost  25  yards  of  sheeting,  at  ^5  of  a  dol- 
lar pei*  yard  ? 

21.  If  it  costs  Jg  of  a  dollar  to  build  a  rod  of  wall, 
what  will  it  cost  to  build  20  rods  ? 

22.  If  a  boy  runs  ||  of  a  rod  in  1  second,  how  many 
rods,  at  the  same  rate,  will  he  run  in  15  seconds  ? 

23.  If  a  locomotive  runs  f  f  of  a  mile  in  1  minute, 
how  far  will  it  run  in  75  minutes  ? 

24.  If  2  bushels  of  apples  cost  f  of  a  dollar,  what 
will  1  bushel  cost  ? 

Solution.  One  bushel  will  cost  1  half  as  much  as  2 
bushels  ;  1  half  of  f  of  a  dollar  is  f  of  a  dollar  ;  there- 
fore, if  2  bushels  cost  f  of  a  dollar,  1  bushel  will  cost 
^  of  a  dollar. 

NOTE.  To  find  J  of  a  number  is  the  same  as  to  divide  the 
number  by  2.  It  is  just  as  evident  that  J-  of  &.  is  2.,  as  it  is  that 
£  of  6  cents  is  3  cents.  Hence,  dividing  the  numerator  of  a  frac- 
tion by  any  number,  is  dividing  the  fraction  by  the  same  number. 

25.  If  a  boy  walks  3  miles  in  f  of  an  hour,  how 
long  will  it  take  him  to  walk  1  mile  ? 

26.  What  is  £  of  f  ?     Am.  f  -j-  3  =  f 

27.  If  4  men  can  reap  T\  of  an  acre  of  rye  in  an 
hour,  how  much  can  1  man  reap  in  the  same  time  ? 

28.  If  a  boy  can  run  £f  of  a  mile  in  3  minutes,  how 
far  can  he  run  in  1  minute  ? 

29.  What  is  1  dozen  of  eggs  worth,  if  7  dozen  are 
worth  |f  of  a  dollar  ? 

30.  What  is  \  of  if  ?     Am.  |f  -f-  7  =  &. 

31.  What  is  -ft  -^  2  ?   |f  -f-  4  ?    f  §  -5-  5  ? 

32.  What  is  *£  -f-  5  ?   -^  -f-  6  ?   -%°-  -f-  8  ? 

33.  Hannah  divided  one  third  of  a  pie  equally  be- 
tween 2  children  ;  what  part  of  the  whole  pie  did  she 
give  to  each  child  ? 


LES.  II.]  ARITHMETIC.  127 

Solution.  One  third  equals  f  ,  and  \  of  £  is  \  ;  that 
is>  i  of  ^  is  J  ;  and  therefore  she  gave  \  of  the  whole 
pie  to  each  ? 

NOTE.  Multiplying  the  denominator  by  2  makes  twice  as 
many  parts  in  the  unit,  and  therefore  each  part  is  only  one  half 
as  great  ;  hence,  multiplying  the  denominator  by  any  number  ,  divides 
the  fraction  by  the  same  number. 

34.  Three  fifths  of  a  barrel  of  flour  were  divided 
equally  among  4  poor  families  ;  what  part  of  a  barrel 
did  'each  receive  ? 

35.  If  £  of  a  bushel  of  chestnuts  are  divided  equally 
among  5  boys,  what  part  of  a  bushel  does  each  re- 
ceive ? 

36.  What  is  1  sixth  of  f  ?    1  eighth  of  $  ? 

37.  What  is  1  ninth  of  f  ?    1  twelfth  of  T7T  ? 

38.  Mary  having  a  nice  large  pineapple,  gave  ^. 
of  it  to  Sarah,  ^  to  Fanny,  ^  to  Laura,  and  kept 
the  rest  herself;  what  part  of  the  pineapple  did  she 
give  away  ?     What  part  did  she  keep  ? 

39.  Whatis^  +  A  +  A? 

40.  What  is  H  —  A?    «  —  A? 

41.  WhatiSlV 

42.  What  is 


LESSON  II. 

1.  ONE  half  is  equal  to  how  many  sixths  ? 
Solution.  Since  f  make  a  whole  one,  ^  of  a  whole 

one  will  be  ^  of  f  ,  which  is  f  ;  therefore,  etc. 

2.  One  third  of  an  apple  is    equal  to  how  many 
sixths  of  an  apple  ? 

3.  James  gave  ^  of  a  pear  to  William,  ^  to  George, 
and  kept  the  rest  himself;    how  much  did   he   give 
away  ?     How  much  did  he  keep  ? 

NOTE.  Change  the  fractions  to  sixths.  Before  fractions  that 
have  different  denominators  can  be  added  together,  or  before  one 
can  be  subtracted  from  another,  it  is  necessary  to  change  them 
to  other  fractions  that  have  like  denominators. 


123  INTELLECTUAL  [SEC.  VII. 


4.  £  +  £  =  what?    1  —  #  =  what? 

5.  A  man  gave  J  of  a  dollar  to  one  of  his  work- 
men, and  f  of  a  dollar  to  another  ;  how  many  fourths 
of  a  dollar  did  he  give  to  both  ?    How  many  dollars  ? 

6*  2"  ~\~  f  are  now  many  i  ?     How  many  times  1  ? 
NOTE.    Read  the  first  question  in  Ex.  6  as  follows  ;  One  half 
and  three  fourths  are  how  many  fourths  ~?     Head  all  similar  ex- 
amples in  like  manner. 

7.  A  man  gave  J  of  a  barrel  of  apples  to  one  of 
his  neighbors,  and  f  of  a  barrel  to  another  ;  did  he 
give  more  to  one  than  to  the  other  ? 

8.  £  and  f  are  how  many  ^  ?     How  many  times  1  ? 

9.  Henry  gave  ^  of  an  orange  to  his  brother  John, 
$   to   his  sister  Marion,  and   kept  the   rest   himself. 
With  this  division  the  selfish   John  was  dissatisfied, 
saying  that  Henry  had  given  more  to  Marion  than  to 
him.      No,  John,  said  Marion,  Henry  has  given  just 
as  much  to  you.  as  to  me,     Now  which  was  right, 
John  or  Marion  ?     What  part  of  the  orange  did  Henry 
keep  for  himself? 

10.  ^  is  how  many  J  ? 

11.  ^  -|-  §  -{-  J  —  how  many  £  ?  How  many  times  ]  ? 

12.  Samuel  worked  f  of  a  day  for  Mr.  Adams,  and 
f  of  a  day  for  Mr.  Daniels.     Mr.  Adams  paid  Samuel 
50  cents.    Now,  at  the  same  rate,  what  should  Mr. 
Daniels  pay  him  ?     How  much,  at  that  Kite,  will  Sam- 
uel earn  in  a  day  ?     What  part  of  a  dollar  ? 

13.  §  are  how  many  J  ? 

14.  A  boy  wished  to  give  ^  of  a  pear  to  his  sister, 
and  ^  to  his  brother  ;  and  in  order  to  do  this  most  con- 
veniently, he  first  cut  the  pear  into  6  equal  pieces  ; 
how  many  pieces  did  he  give  to  each  ?     Plow  many 
pieces  had  he  remaining  ? 

15.  Samuel  gave  -J  of  a  dollar  to  one  poor  boy,  and 
-J  of  a  dollar  to  another  ;  what  part  of  a  dollar  did  lie 
give  away  ?     How  much  more  to  one  boy  than  to  thtj 
other  ? 


LES.  II.]  ARITHMETIC.  129 

16.  What  is  J+J?    £  — J? 

17.  James  had  a  box  of  strawberries,  and  said  he 
would  give  J  of  them  to  Addie,  J-  to  Willie,  and  the 
rest  to  Georgie,  if  he  could  tell  how  to  divide  them. 
Georgie  won  ;  how  did  he  divide  them  ? 

18.  Harriet  having  3  quarts  of  cherries,  said  she 
would  give   f  of  a  quart  to  Mary,  f  of  a  quart  to 
Martha,  and  the  rest  to  any  one  of  the  company  who 
would  most  quickly  tell  how  to  divide  them.  Would  you 
have  won  had  you  been  there,  and  how  would  you 
divide  them? 

19.  I  are  how  many  £  ?    3  are  how  many  J-  ? 
20-  I  +  f  ==  how  many  £  ?    3  —  J#  =  what  ? 

21.  A  man  having  2  bushels  of  wheat  to  give  to  3 
of  his  workmen,  wished  to  give  |  of  a  bushel  to  the 
first,  f  of  a  bushel  to  the  second,  and  the  rest  to  the 
third  ;  how  much  should  he  give  to  the  third  ? 

22.  §  are  how  many  -fa  ?    £  are  how  many  -fa  ? 

23.  A  farmer  had  a  horse,  a  cow,  and   a  sheep. 
The  horse  would  eat  §  of  a  ton  of  hay  in  a  month,  the 
cow  r3¥,  and  the  sheep  •£$ ;  how  much  would  they  all 
eat?     How  much  more  would  the  horse  eat  than  the 
sheep  ?     How  much  less  would  the  sheep  eat  than  the 
cow? 

24.  |  are  how  many  ^  ?    T%-  are  how  many  ?V  ? 

25.  A  man  gave  f  of  a  ton  of  coal  to  B,  and  f  of  a 
ton  to  C  ;  to  which  did  he  give  the  most  ?     How  much  ? 
How  much  to  both  ? 

26.  A  little  girl  having  a  pound  of  figs,  gave  f  of 
them  to  one  schoolmate,  -f^  to  another,  and  kept  the 
rest;  what  part  of  the  pound   did  she  give  away? 
What  part  did  she  keep  ? 

27.  |  are  how  many  •£$  ?    -f^  are  how  many  3V  ? 

28.  A  spendthrift  having  received  a  fortune,  squan- 
dered TV  of  it  the  first  month,  and  fo  of  it  the  next 
month,  after  receiving  it ;  what  part  of  it  had  he  then 


remaining  ? 


9 


130  INTELLECTUAL  [SEC.  VII. 

LESSON  HI. 

1.  REDUCE  f  to  its  lowest  terms.    Ans.  J. 

2.  Reduce  £  to  its  lowest  terms. 

3.  Reduce  f  to  its  lowest  terms* 

4.  Reduce  f  to  its  lowest  terms. 

5.  Reduce  -f%  to  its  lowest  terms. 

6.  Reduce  -fy  to  its  lowest  terms. 

7.  Reduce  |£  to  its  lowest  terms. 

8.  Reduce  -f^  to  its  lowest  terms. 

9.  Reduce  |f  to  its  lowest  terms    * 

10.  Reduce  -f-§  to  *ts  lowest  terms. 

11.  Reduce  ^r  to  its  lowest  terms. 

12.  Reduce  f  f  to  its  lowest  terms. 

13.  Reduce  j|  to  its  lowest  terms. 

14.  Reduce  J£  to  its  lowest  terms. 

15.  Reduce  £f  to  its  lowest  terms. 

16.  Reduce  f  f  to  its  lowest  terms. 

17.  Reduce  f  £  to  its  lowest  terms. 

18.  Reduce  f  J  to  its  lowest  terms. 

19.  Reduce  ^  to  twelfths.     |  to  twelfths. 

20.  Reduce  f  to  twelfths,     f  to  twelfths. 

21.  Reduce  -j%  to  fifths,     f  to  twentieths. 

22.  Reduce  -f$  to  fourths,     f  to  twentieths. 

23.  Reduce  f  and  f  to  equivalent  fractions  having 
a  common  denominator. 

24.  Reduce  ^  and  -fa  so  that  they  shall  have  the 
least  common  denominator. 

25.  Reduce  f  and  f .     -fa  and  Jf. 

26.  Reduce  f  and  j.     ft  and  |§. 

27.  Reduce  f  and  | .     Jf  arid  f  |. 

28.  Reduce  ^,  £,  and  J,  so  that  they  shall  have  the 
least  common  denominator. 

29.  Reduce  f ,  •&,  and  &• 

30.  Reduce  |,  |,  and  J. 

31.  Add  together  J-  and  £.     |  and  f. 

32.  Add  together  f  and  §.     £  and  J. 


LES.  IV.]  ARITHMETIC.  131 

33.  Add  together  f  and  £.     fg-  and  j-f . 

34.  Add  together  J,  |,  and  TV     f ,  A,  and  |f . 

35.  Subtract  £  from  £.     £  from  §. 

36.  Subtract  ^  from  j.     f  from  T9Q. 

37.  Subtract  f  from  f.     f  from  -fa. 

38.  Subtract  f  from  f .     f  from  {%. 

39.  A  and  B  engage  to  do  a  piece  of  work.     A  can 
do  %  of  it  in  a  day,  and  B  can  do  £  of  it ;  what  part 
of  the  work  can  they  together  do  in  a  day  ?     What 
part  of  it  would  remain  for  the  next  day  ?     What  part 
of  the  next  day  would  it  take  them  to  finish  the  work  .' 

40.  A,  B,  and  C  engage  to  do  a  piece  of  work.     A 
can  do  -J  of  it  in  a  day,  B  can  do  §  of  it,  and  C  can  do 
£  of  it ;  what  part  of  the  work  can  they  all  do  in  a  day  ? 
What  part  would  remain  for  the  next  day?     What 
part  of  the  second  day  would  it  take  them  to  finish  tiio 
work  ? 

41.  -fa  is  what  part  of  -£$  ?     -f$  what  part  of  |J  ? 

LESSON  IV. 

1.  A  EOT  having  J  of  an  apple,  gave  away  J  of 
that ;  what  part  of  the  whole  apple  did  he  give  away  ? 

2.  What  is  i  of  i  ?    J  is  how  many  J  ? 

3.  A  boy  having  ^  of  a  melon,  gave  away  ^  of 
that ;  what  part  of  the  whole  melon  did  he  give  away  ? 
What  part  did  he  keep  ? 

4.  What  is  £  of  £?    i  — iof  £? 

5.  James  having  £  of  a  clay  for  play,  spent  ^  of 
that  time  with  his  cousin  Alfred  ;  what  part  of  the 
whole  day  was  he  with  Alfred  ? 

6.  What  is  lof  i?    lof  i? 

7.  A  man  having  ^  of  a  cord  of  wood,  gave  away 
J  of  that ;  what  part  of  a  cord  did  he  give  -  away  ? 
Wliat  part  did  he  keep  ? 

8.  What  is  I  of  £?    f  of  J? 

Ans.  I  of  \  is  \  ;  and  f  of  \  is  3  times  £,  or  |. 


132  INTELLECTUAL  [SEC.  VII. 

0.  A  man  having  J  of  a  cord  of  wood,  gave  away 
J  of  that,  and  sold  the  rest ;  what  part  of  a  cord  did 
he  give  away  ?  What  part  did  he  sell  ? 

10.  What  is  i  of  J? 

11.  Which  is  the  most,  J  of  J,  or  £  of  J? 

12.  What  is.  J  of  J?    Jof  i? 

13.  A  merchant  owning  £  of  a  ship,  sold  ^  of  his 
share  ;  what  part  of  the  ship  did  he  sell  ?   What  part 
did  he  keep  ? 

14.  What  is  i  of  i?    f  of  £  ? 

15.  What  is  i  of  J?    f  of  J? 

16.  What  is  J  of  |?    f  of  |  ? 

17.  What  is  £  of  £  ?    £  of  £  ?       * 

18.  A  boy  having  f  of  a  melon,  gave  away  |  of  - 
what  he  had ;  what  part  of  a  whole  melon  did  he  give 
away? 

Solution.  If  £  of  a  melon  is  cut  into  2  equal  parts,  each 
part  is  \  of  the  whole  melon  ;  and  if  £  of  J  is  ;J>  then 
\f  of  -j  is  § ;  therefore,  he  gave  away  f  of  the  whote 
melon.  ,  /  « 

19.  A  man-  owning  f  of  a  ship,  sold  f,  of  his  share* 
what  part  of  the  whole  ship  did  he  sell  ? 

20.  A  girl  having  picked  f  of  a  pailful  of  blueber- 
ries, spilled  4  of  tij^m  ;  what  part  of  a  pailful  did  she 
spill? 

21.  A  boy  having  f  of  a  dollar,  lost  £  of  what  he 
ha'd*  what  part  of  a  dollar  did  he  lose  ? 

22.  What  is  i  of  f  ?    i  off?    |  of -ft? 

i     23.  What  is  ^  of  |  ?    J  of  $  ?    A  of  £? 

24.  -WhatisiofT7T?    }of£?    TV°ff?  , 
•    25.  A  boy  having  f  of  a  pear,  gave  away  f  of  what 
he  had.;  what  part  of  a  whole  pear  did  he  give  away  ?, 

Solution.  %  of  £  is  TV  ;  therefore,  J  of  f  is  -fg  ;  and  if 
j.of  f  is 'TV  then  ff  of>  f  is  2  times  A»  which  are  T8^ ; 
therefore,  he  gave  away  T8^  of  the  whole  pear. 

26.  Charles  had  J  of  a  dollar,  and  gave  f  of  that 
for  a  knife  ;  \vliat  part  of  a  dollar  did  the  knifb  cost  ?  • 


LES.  IV.]  ARITHMETIC.  133 

27.  If  a  yard  of  lace  is  worth  £  of  a  dollar,  what 
are  J  of  a  yard  worth  ? 

•    28.   What  cost  §  of  a  bushel  of  corn,  at  ^  of  a  dollar 
per  bushel  ? 

29.  A  man  owning  |  of  a  ship,  sold  f  of  his  share ; 
what  part  of  the  whole  ship  did  he  sell  ?     What  part 
did  he  keep  ? 

30.  If  a  boy  can  pick  f  of  a  bushel  of  chestnuts  in 
a  day,  what  part  of  a  bushel  can  he  pick  in  f  of  a 
day  ? 

31.  If  a  man  can  reap  |  of  an  acre  of  wheat  in  a 
day,  what  part  of  an  acre  can  he  reap  in  f  of  a  day  ? 

Solution.  In  i  of  a  day  he  can  reap  \  of  f ,  which  is 
.  ^  of  an  acre ;  ana  in  f  of  a  day  he  can  reap  5  times  ^, 
Vhich  are  f,  of  an  acre. 

32.  What  cost  f  of  a  bushel  of  butternuts,  at  ^  of  a 
•dollar  per  bushel  ? 

.''    63.  What  cost  £  of  a  bushel  of  corn,  at  ff  of  a  dol- 
lar per  bushel  ? 
^  34.  If  ^  man  can  mow  J-g-  of  an  acre  of  grass  in  an 

*heiirt  what  part  of  an  acre  can  he  mow  in  f  of  an 
hour? 

35.  If  a  dozen  of  oranges  are  worth  |f  of  a  dollar, 
.  what  are  f  of  a  dozen  worth  ?       9 

36.  At  |f  of  a  dollar  per  day,  what  will  a  man 
'  earn  in  f  of  a  day  ? 

37.  If  a  boy  learns  T87  of  his. lesson  in  an  hourr 
what  part  of  it  does  he  learn  in  -J  of  an  hour  ? 

3$.  At  J|  of  a  dollar  per  rod,  what  will  it  cost  to 
build  f  of  a  rod  of  fence  ? 

39.  A  man  owning  |-  of  a  ship,  sold  ^  of  his  share ; 
how  many  thirds  of  the  ship  did  he  sell  ? 

40.  What  is  J-  of  §  ? .  . 

41.  A  man  owning  -J  of  a  farm,  sold  J  of  his  share  ; 
what  part  of  the  farm  did  he  sell  ?     What  part  did 
he  keep  ?  . 

,      42.  What  is  i  of  f  ?    f  of  f  ? 


13  i  INTELLECTUAL  [SEC.  VII. 

43.  What  is  £  of  £  ?    £  of  f  ? 

44.  What  is  I  of  f  ?    §  of  ?  ? 

45.  What  is  -J  of  ff  ?    f  of  fj  ? 

46.  What  is  £  of  ^  ?    |  of  j  f  ? 

47.  What  is  £  of  |  of  f  ? 

Solution.  J  of  |-  is  £  ;  £  of  f  is  J  ;  therefore,  J  of 
§  of  }  is  J. 

48.  What  is  £  of  §  of  |  of  £  of  £  of -f  of  £  of  f  ? 
41).  A   girl    wishing   to  divide    £    of  a   pineapple 

equally  among  her  3  brothers,  was  at  a  loss  to  know 
how  to  divide  it.  At  length  she  decided  to  cut  each 
of  the  fifths  into  3  equal  parts  ;  how  many  pieces  did 
she  give  each  of  the  boys  ?  What  part  of  the  pine- 
apple was  each  piece  ? 

50.  The  gi^l  mentioned  in  the  above  example 
could  have  made  a  better  division  of  the  f  of  a  pine- 
apple ;  can  you  tell  how  ?  By  your  plan,  how  many 
pieces  would  you  give  to  each  boy  ?  What  would  be 
the  size  of  the  pieces  ? 

LESSON  V. 

1.  IF  a  barrel  of  apples  cost  2J  dollars,  what  will  J 
of  a  barrel  cost  ? 

2.  What  is  i  of  2J  ? 

Solution.  ^  of  2  is  1  ;  \  of  J  is  £  ;  therefore,  J  of 
2i  is  1J. 

3.  If  3  barrels  of  flour  cost  $21|,  what  is  the  price 
per  barrel ? 

4.  What  is  J  of  21 J? 

5.  A  lady  divided  8f  pounds  of  maple  sugar  equally 
among  her  4  children  ;  how  much  did  she  give  to  each  ? 

6.  What  is  J  of  8|  ? 

7.  A   boy  divided  2J  oranges    equally  among   his 
brother,  his  sister,  and  himself;  what  part  of  an  or- 
ange did  each  have  ? 

8.  What  is  £  of  2  J-  ? 


LES.  V.]  AKITHMETIC.  135 

Solution.  2J  are  the  same  as  f,  and  J  of  f  is  f  ; 
therefore,  J  of  2£  is  £ . 

9.  If  4  gallons  of  molasses  cost  $3J,  what  dqes  1 
gallon  cost  ? 

10.  What  is  £  of  3J? 

11.  If  6  bushels  of  oats  cost  $3f,  what  is  the  price 
per  bushel  ? 

12.  What  is  i  of  3  J-  ? 

13.  Paid  $7J  for  10  yards  of  cloth ;  what  did  I 
pay  for  1  yard  ? 

14.  What  is  Jt  of  7}  ? 

15.  Bought  12  bushels  of  corn  for  $llf  ;  what  did 
it  cost  per  bushel  ? 

16.  What  is  £f  of  llf  ? 

17.  If  5  bushels  of  wheat  cost  $8f,  what  is  the 
price  per  bushel  ? 

18.  What  is  J-  of  8|  ? 

Solution.  8f  equals  %5-,  and  £  of  ^5-  is  f ,  or  If. 
Or,  5  in  8},  once  and  3f  over ;  3f  equals  ±f-,  and 
£  of  *f-  is  f ,  which,  added  to  the  1,  gives  If. 

19.  A  man  bought  6  pounds  of  cheese  for  62 £  cents, 
what  did  he  pay  per  pound  ? 

20.  What  is  £  of  62  j  ?    £  of  74f  ? 

21.  If  7  barrels  of  flour  cost  60f  dollars,  what  is  the 
price  per  barrel  ?     What  is  the  cost  of  2  barrels  ? 

22.  What  is  |  of  60f  ?    f  of  60J  ? 

23.  A  man  bought  a  cow  for  $33^,  and  afterward 
sold  her  for  |  of  her  cost ;  how  many  dollars  did  he 
gain  ?     What  did  he  receive  for  her  ? 

24.  What  is  J  of  33^  ?   |  of  33 J  ? 

25.  A  man  bought  a  horse  for  $65f  ;  but,  not  prov- 
ing so  good  as  he  anticipated,  he  sold  it  for  £  of  its 
cost ;  how  much  did  he  lose  ?     For  how  many  dollars 
did  he  sell  it  ? 

26.  What  is  £  of  65f  ?    J  of  65$  ? 

27.  If  1  man  can  do  a  piece  of  work  in  27f  days, 
how  long  would  it  take  4  men  to  do  the-  same  ? 


136  INTELLECTUAL  [SEC.  VII. 

28.  What  is  J  of  27}  ?    i  of  i  of  27}  ? 
20.  If  a  horse  can  travel  27f  miles   in  4   hourSj 
how  far,  at  the  same  rate,  can  he  travel  in  9  hours  ? 

30.  What  is  i  of  27$  ?  J  of  27  J  ? 

31.  If  7  yards  of  cloth  cost  $31  f,  what  will  5  yards 
cost? 

32.  What  is  }  of  31§  ?    £  of  31§  ? 

33.  If  4  pipes  will  empty  a  cistern  containing  38g 
gallons  in  a  given   time,  how  many  gallons  will  be 
drawn  from  the  cistern  by  3  pipes  of  the  same  size  in 
the  same  time  ? 

34.  What  is  J  of  '38$  ?    }  of  38  j-  ? 

35.  If  3  horses  eat  22£  bushels  of  oats  in  8  weeks, 
what  will  7  horses  eat  in  the  same  time  ? 

36.  What  is  J  of  22J-  ?    f  of  18f  ? 

37.  In  a  freshet,  a  tree  stood  so  that  35§  feet,  which 
were  f  of  its  entire  length,  were  under  water ;  how 
many  feet  were  above  water  ?     What  was  the  whole 
length  of  the  tree  ? 

38.  What  is  f  of  35§  ?    J  of  35f  ? 

39.  A  man  distributed  23 f  bushels  of  wheat  equally 
among   7  poor  families  ;    how  many  bushels,  at   the 
same  rate,  would  have  been  required  for  9  families  ? 

40.  What  is  f  of  23 f  ?   £  of  13f  ? 

41.  If  8  soldiers  are  allowed  13  J  pounds  of  meat 
in  1  day,  what  will  3  soldiers  be  allowed  in  5  days  ? 

42.  What  is  5  times  f  of  13  J? 

43.  What  is  4  times  f  of  19J  ? 

LESSON  VI. 

1.  A  BOY  having  2  melons,  ate  £  of  a  melon  each 
day  as  long  as  they  lasted ;  how  many  days  did  they 
last  ?     How  many  days  would  they  have  lasted  had 
he  eaten  §  of  a  melon  each  day  ? 

2.  How  many  times  is  -^  contained  in  2  ;  that  is 
how  many  tunes  is  J  contained  in  §  ? 


LES.  VI.]  ARITHMETIC.  137 

Solution.  6  times';  for  2  equals  f ,  and  J  is  contained 
in  §  just  as  many  times  as  1  apple  is  contained  in  6 
apples,  or  as  1  is  contained  in  6. 

3.  How  many  times  §  in  '2  ? 

Solution.  3  times;  for  ^  is  contained  in  f.  just  as 
many  times  as  2  in  6.  Or,  since  J  is  contained  6  times 
in  f ,  f  is  contained  J  of  6  times,  viz.,  3  times,  in  f . 

4.  A  boy  having  3  oranges,  gave  f  of  an  orange 
f  piece  to  several  of  his  companions ;  to  how  many 
could  he  give  them  ? 

5.  How  many  times  J  in  3  ?    f  in  3  ? 

6.  If  f  of  a  pound  of  butter  will  last  a  family  1 
day,  how  many  days  will  4  pounds  last  the  same  fam- 
ily ?    How  many  days  will  6  pounds  last  ?   7  pounds  ? 

7.  How  many  times  §  in  4  ?     In  6  ?     In  7  ? 

8.  If  f  of  a  barrel  of  apples  will  supply  a  family 
for  a  week,  for  how  many  weeks  will  6  barrels  supply 
the  same  family  ?     For  how  many  weeks  will  6  barrels 
supply  them,  if  they  use  f  of  a  barrel  a  week  ?     If 
they  use  f  ? 

9.  In  6  how  many  times  f  ?    f  ?    f  ? 

10.  If  a  family  consumes  J  of  a  barrel  of  flour  in  a 
month,  how  long  will  3-f  barrels  last  them  ?    9 1  bar- 
rels ?    8i? 

11.  How  many  times  f  in  3f  ?     In  9|  ?    8J  ? 

12.  How  long  will  9  pounds  of  butter  last  a  family, 
if  they  use  1^  pounds  per  week? 

13.  How  many  times  1J-,  or  f  in  9  ? 

14.  How  many  soldiers  will  8-|  founds  of  bread 
supply,  if  each  soldier  is  allowed  1|  pounds? 

15.  In  8J  how  many  times  If  ? 

16.  How  many  garments  will  20 J  yards  of  cloth 
make,  if  each  garment  requires  2J  yards  ? 

17.  In  20 J  how  many  times  2^  ? 

18.  When  raisins  cost  ^  of  a  dollar  a  pound,  IIOTV 
many  pounds  can  you  buy  for  f  of  a  dollar  ? 

19.  How  many  times  is  £  contained  in  J  ? 


133  INTELLECTUAL  [SEC.  VII. 

Solution.  |  are  the  same  as  -f%,  and  £  equals  -^  ;  ^ 
in  -f^y  4£  times  ;  therefore,  J  in  f  ,  4J  times. 

20.  When   cream  of  tartar  costs  f  of  a  dollar  a 
pound,  how  many  pounds   may  be  bought  for  $1£? 
How  many  for  $2f  ? 

21.  How  many  times  £  in  1  £  ?     In  2f  ? 

22.  At  f  of  a  dollar  per  pound,  how  many  pounds 
of  tea  can  1  buy  for  $2£  ?    For  $3J  ? 

23.  How  many  times  £  in  2J-  ?     In  3J  ? 

24.  If  coffee  costs  J  of  a  dollar  a  pound,  how  many 
pounds  may  be  bought  for  $1£  ?     For  $2$  ? 

25.  How  many  times  f  in  1  £  ?     In  2§? 

26.  At  $1  J  per  bushel,  how  much  wheat  can  I  buy 
for  $3J  ?     For  $5fc  ? 

27.  How  many  times  1  J  in  3£  ?   In 


28.  At  $2J  a  box,  how  many  boxes  of  raisins  can 
you  buy  for  $6J  ?     For  ?9|  ? 

29.  How  many  times  2£  in  6f  ?     In  9|  ? 

30.  At  8J  cents  a  pound,  how  many  pounds  of  su- 
gar can  I  buy  for  12^  cents  ?     For  33£  cents  ? 

31.  How  many  times  8J  in  12^  ?     In  33£  ? 

32.  How  many  times  6£  in  37^  ?     In  87£  ? 

33.  How  many  times  5|  in  6T\  ?     In  7  £  ? 

34.  If  3£  barrels  of  flour  cost  $20f  ,  what  will  6J 
barrels  cost? 

Suggestion.  6f  is  twice  3f. 

35.  If  5|  barrels  of  apples  cost  $11^,  what  will  28| 
barrels  cost? 

36.  If  2|  acres  of  land  are  worth  $26,  what  are  10| 
acres  worth  ? 

37.  If  7|  acres  of  land  cost  $28f,  what  will  5J 
acres  cost  ? 

Suggestion.  7f  in  28f  ,  4  times. 

38.  If  2J  pounds  of  veal  cost  24|  cents,  what  will 
5J   pounds   cost?    lOf    pounds?    21  J    pounds?    7f 
pounds  ? 


LES.  I.J  ARITHMETIC. 

SECTION  EIGHTH. 
LESSON  I. 

REMARKS.  1.  Per  centum,  or  per  cent.,  is  an  ex- 
pression which  means  by  the  hundred ;  thus,  5  per 
cent,  of  any  number  is  T^  or  ^  of  that  number;  25 
per  cent,  is  T2<y5<j  or  |  ;  3  per  cent,  is  T-g-7,  etc. 

2.  Gains  and  losses,  interest   on  money,  commis- 
sions of  agents,  increase  or  decrease  of  population,  etc., 
are  usually  computed  at  some  given  per  cent,  on  the 
sum  or  number  considered. 

3.  The  following   rates,  being  readily  reduced  to 
convenient  fractional  forms,  are  easily  computed  : 

2  per  cent,  is      .     .     •£$.   12 £  per  cent,  is      .     .     J. 

5     «      '.  ".  *.  1C  20*    «       !  !  !  f. 

25         «  .     .     .     J. 

33J       «  ...     4. 

10"       «          ...     TV  50         «  ...     4. 

Ex.  1.  A  farmer  having  80  sheep,  lost  25  per  cent, 
of  them  ;  how  many  sheep  did  he  lose  ? 

Solution.  He  lost  -ff^  or  ^  of  his  flock  ;  ^  of  80  is 
20  ;  therefore,  he  lost  20  sheep. 

2.  The  number  of  inhabitants  in  the  town  of  B  on 
the  1st  of  May,  1860,  was  2500  ;  in  a  year  the  popu- 
lation increased  20  per  cent.  ;  what  was  the  increase 
of  population  in  the  year  ?     What  was  the  population 
of  B  on  the  1st  of  May,  1861  ? 

3.  An  agent  sells  $500  worth  of  goods  for  his  em- 
ployer, and  receives  a  commission,  or  compensation,  of 
4  per  cent,  for  transacting  the  business  ;   how  many 
dollars  does  he  receive  for  his  services  ?     How  many 
dollars  does  he  pay  over  to  his  employer  ? 

4.  In  one  town  in  Wisconsin  16000  bushels  of  wheat 
grew  in  1863  ;  what  will  be  the  number  of  bushels  in 
1864,  if  there  shall  be  a  decrease  of  12  £  per  cent.  ? 


A- 


14)  INTELLECTUAL  [SEC.  VIII. 

5.  A  physician  having  bills  against  his  patients  to 
the  amount  of  $72,  paid  1G|  per  cent,  for  their  col- 
liviion  ;  what  did  the  agent  receive  for  collecting  the 
money  ?     What  did  he  pay  over  to  the  physician  ? 

6.  Suppose  the  number  of  deaths  in  New  York  dur- 
ing the  1st  week  of  March  was  500,  and  that  the  de- 
crease during  the  1st  week  of  June  was  10  per  cent. ; 
how  many  less  deaths  were  there  in  the  city  during 
the  latter  week  ?     What  was  the  number  of  deaths 
during  the  latter  week  ? 

7.  The  American  Insurance  Company  has  insured 
$4000  on  my  house,  at  a  premium  of  2  per  cent. ;  what 
is  the  premium,  or  sum  paid  for  the  insurance  ? 

8.  What  is  GJ  per  cent,  of  $64  ? 

9.  What  is  33  J  per  cent,  of  45  bushels  of  corn  ? 

10.  What  is  5  per  cent,  of  80  peaches  ? 

1 1.  What  is  8  J  per  cent,  of  48  boys  ? 

12.  What  is  50  per  cent,  of  36  horses  ? 

13.  A  physician  having  bills  against  his  patients  to 
the  amount  of  $80,  paid  $20  for  collecting  them ;  what 
per  cent,  did  he  pay  ? 

Solution.  $80  is  100  per  cent.,  or  the  whole  sum 
collected,  and  $20  is  f  §  or  \  of  the  whole  sum ;  ^  of 
100  per  cent,  is  25  per  cent. ;  therefore,  etc. 

14.  In  a  lot  of  60  barrels  of  apples,  12  barrels  are 
spoiled  and  the  rest  are  good ;  what  per  cent,  of  them 
are  spoiled  ?     What  per  cent,  are  good  ? 

15.  From  a  cask  of  63  gallons  of  molasses,  a  grocer 
has  drawn  21  gallons  ;  what  per  cent,  of  the  molasses 
has  he  drawn  out  ?     What  per  cent,  of  it  remains  in  ? 

16.  What  per  cent,  do  I  gain  by  buying  hats  at  $4, 
and  selling  them  at  $5,  apiece  ? 

17.  What  per  cent,  do  I  lose  by  buying  hats  at  $5, 
and  selling  them  at  $4,  apiece  ? 

J  8.  Twenty  is  what  per  cent,  of  50  ? 
10.  A  gentleman  invested  f  of  his  money  in  land; 
what  per  cent,  of  it  did  he  so  invest  ? 


LES.L]  ARITHMETIC.  141 

Solution.  The  whole  of  any  thing  is  100  per  cent,  of 
it ;  hence  f  of  the  thing  is  f  of  100  per  cent.,  which  is 
40  per  cent. ;  therefore,  etc. 

20.  A  man  saved  §  of  his  income,  and  spent  the  rest ; 
what  per  cent,  of  it  did  he  save  ?     What  per  cent, 
did  he  spend  ? 

21.  Three  fourths  of  a  number  is  what  per  cent,  of  it  ? 

22.  Seven  eighths  of  a  number  is  what  per  cent,  of  it  ? 

23.  Five  sixths  of  a  number  is  what  per  cent,  of  it  ? 

24.  At  5  per  cent.,  what  sum  can  be  insured  on  a 
ship  bound  from  Boston  to  San  Francisco,  for  a  pre- 
mium of  $GO  ? 

Solution.  Since  5  per  cent,  is  T^  or  -fa  of  the  sum 
insured,  the  premium,  $00,  is  ^  of  the  sum  insured ; 
$60  is  Jfr  of  $1200  ;  therefore,  etc. 

25.  At  2  per  cent,  what  sum  can  be  insured  on  a 
house  for  a  premium  of  $50  ? 

26.  $24  is  16f  per  cent,  of  what  sum? 

27.  Seven  oranges  are  25  per  cent,  of  what? 

28.  In  1863,  a  farmer  raised  63  bushels  of  corn  on 
an  acre.     This  was  an  increase  of  12  J  per  cent,  on  the 
previous  year's  crop  ;  how  many  bushels  did  he  raise 
on  the  acre  in  1862  ? 

Solution.  Since  the  increase  was  12  J  per  cent.,  or  |, 
of  the  crop,  63  bushels  is  f  of  the  crop  ;  63  bushels  is 
|  of  56  bushels  ;  therefore,  the  crop  of  1862  was  56 
bushels  to  the  acre. 

29.  A  grocer  sold  tea  at  50  cents  per  pound,  and 
thereby  gained  25  per  cent,  on  the  cost ;  what  was  the 
cost  per  pound  ? 

30.  A  grocer  sold  tea  at  45   cents  per  pound,  and 
thereby  lost  25  per  cent,  on  the  cost ;  what  was  the 
cost  per  pound  ? 

31.  A  merchant  sends  his  agent  $42,  from  which  he 
is  to  take  a  commission  and  expend  the  rest  for  coffee. 
The  agent's  commission  being  5  per  cent,  on  the  pur- 
chase, what  sum  will  he  have  to  expend  ? 


112  INTELLECTUAL  [SEC.  VIII. 

Solution.  The  sum  to  be  expended  is  -}-gg-  of  itself, 
and  the  commission  is  y^  of  the  same  sum ;  hence 
the  sum  sent  to  the  agent  is  -J-g-g-  or  f  £  of  the  sum  ex- 
pended. $42  is  f  £  °*  $40 ;  therefore,  etc. 

32.  A  man  sends  his  agent  in  Oregon  $515,  from 
which  he  is  to  take  a  commission  and  invest  the  bal- 
ance in  land ;  the  commission   being  3  per  cent,  on 
the  purchase,  what  sum  was. invested  in  land  ? 

33.  If  12£  per  cent,  is  gained  by  selling  hay  at  $18 
per  ton,  what  did  it  cost  ? 

34.  If  16f  per  cent,  is  lost  by  selling  a  watch  for 
$40,  what  did  it  cost  ? 

35.  An  agent  retained  a  commission  of  12^  per  cent. 
for  collecting  money,  and  paid   $56  over  to  his  em- 
ployer ;  what  sum  did  he  collect  ? 

Solution.  Since  12 £  per  cent,  or  \  of  the  sum  col- 
lected was  retained  by  the  agent,  the  $56  paid 
over  was  £  of  the  sum  collected.  $56  is  %  of  $64 ; 
therefore,  etc. 

36.  A  farmer  engaged  a  laborer  to  thresh  his  wheat, 
agreeing  to  give  him  10  per  cent,  of  all  he  threshed; 
how  many  bushels  must  he  thresh  that  the  farmer  may 
keep  54  bushels  ? 

37.  If  it  requires  $125  in  paper  currency  to  buy 
$100  in  gold,  how  much  gold  may  be  bought  for  $100 
in  paper  currency  ? 

NOTE.  When  it  takes  more  than  $100  in  bank  bills,  govern- 
ment bonds,  or  other  paper  currency,  to  buy  $100  in  gold,  gold 
is  said  to  be  at  a  premium  if  the  paper  currency  is  taken  as  the 
standard  of  value,  and  the  paper  currency  is  said  to  be  at  a  dis- 
count if  gold  is  taken  as  the  standard. 

38.  If  it  takes  $150  in  paper  currency  to  buy  $100  in 
gold,  what  is  the  per  cent,  of  discount  on  the  paper  ? 

Solution.  The  paper  is  worth  -j-J$  =  §  as  much  as 
gold;  therefore  the  discount  on  the  paper  is  J  =  33J 
per  cent,  of  its  nominal  value. 

39.  If  it  takes  $166|  of  paper  to  buy  $100  in  gold, 


LES.  II.]  ARITHMETIC.  143 

at  what  per  cent,  of  premium  is  gold,  paper  being  ta- 
ken as  the  standard  ?  At  what  per  cent,  of  discount 
is  paper,  gold  being  taken  as  the  standard  ? 


LESSON  U. 

REMARKS.  1.  INTEREST  is  money  paid  for  the  use 
of  borrowed  money.  The  money  borrowed  is  called 
the  Principal.  The  sum  of  the  principal  and  interest 
is  called  the  Amount. 

2.  In  many  of  the  United  States  interest  is  compu- 
ted at  6  per  cent.,  and  this  will  be  the  per  cent,  under- 
stood in  this  book  if  no  other  is  mentioned. 

3.  In    computing   interest,  thirty  days  are  usually 
considered  a  month,  and  12  months  a  year. 

Ex.  1.  The  interest  of  $1  for  a  year  being  6  cents, 
what  is  the  interest  of  $1  for  2  years  ?  For  3  years  ? 
4  years  ?  5  years  ?  8  years  ?  10  years  ?  15  years  ? 

2.  What  is  the  interest  of  a  dollar  for  1  month  ? 
Solution.  Since  the  interest  of  $1  for  12  months  is 

6  cents,  the  interest  of  $1  for  1  month  is  ^  of  6  cents, 
which  is  -f$  or  \  of  a  cent  =  5  mills. 

3.  What  is  the  interest  of  $1  for  2  months  ?     For 
3  months  ?     4  months  ?     6  months  ?     9  months  ?     5 
months?    8   months?    11    months?     10  months?    7 
months  ? 

4.  What  is  the  interest  of  $1  for  lyr.  2m.  ?     For 
lyr.  6m.?    lyr.  3m.  ?    lyr.  8m.  ? 

5.  What  is  the  interest  of  $1  for  2yr.  6m.  ?    2yr. 
3m.  ?    2yr.  10m.  ?    3yr.  4m.  ?    5yr.  7m.  ? 

6.  What  is  the  interest  of  $1  for  6  days  ? 
Solution.  Since  the  interest  of  $1  for  30  days  is  5 

mills,  the  interest  of  $1  for  6  days  is  ^  or  £  of  o 
mills,  which  is  1  mill. 

7.  What  is  the  interest  of  $1  for  12  days?     For 
18  days?    24  days?    1m.  6d.?    1m.  24d.  ?    2m.  ISd.  ? 
4m.  12d.?   7m.  ISd.  ?   8m.  24d.? 


144  INTELLECTUAL  [SEC.  VIIL 

8.  What  is  the  interest  of  $1  for  1  day  ? 
Solution.  Since  the  interest  of  $1  for  G  days  is  1 

mill,  the  interest  of  $1  for  1  day  is  £  of  a  mill. 

9.  What  is  the  interest  of  §1  for  2  days  ?     For  3 
days  ?   4  days  ?   5  days  ?    7  days  ?    8  days  ?     9  days  ? 
15  days?   20  days?    28  days?    19  days? 

10.  What  is  the  interest  of  $1  for  1m.  15d.  ?    2m. 
3d.?   3m.  9d.?   8m.  4d.  ?    7m.  27d.  ?    lyr.  6m.  15d.  ? 

11.  What  is  the  interest  of  $2  for  a  year  ? 
Solution.  Since  the    interest  of  $1  for  a  year   is 

6  cents,  the  interest  of  $2  is  2  times  6  cents,  which 
are  12  cents. 

12.  What  is  the  interest  of  $3  for  a  year?    Of  $4  ? 
Of  $5?   $10?    $12?    $20?    $30? 

13.  What  is  the  interest  of  $2  for  lyr.  6m.  ?    For 
lyr.  6m.  24d.  ?    2yr.  3m.  6d.  ?    Syr.  om.  15d.  ? 

14.  What  is  the  interest  of  $3  for  2yr.  6m.  12d.? 
Of  $5  for  2yr.  3m.  15d.  ?     Of  $10  for  lyr.  7m.  14d.  ? 

15.  What  is  the  interest  of  $100  for  lyr.  ?     For  2 
yr.?    lyr.  6m.?    lyr.  10m.  ?    2yr.  3m.? 

16.  What  is  the  interest  of  $200  for  lyr.?     For 
2yr.  ?    lyr.  4m.  ?    2yr.  6m.  ?    3yr.  2m.  ?    4yr.  8m.  ? 

17.  What  is  the  'interest  of  $50  for    lyr.  ?     For 
2yr.?   5yr.?    6m.?    8m.?    lyr.  4m.  ? 

18.  What  is  the  interest  of  $25  for  lyr.  ?    3yr.  ? 
lyr.  6m.  ?   2yr.  8m.  ? 

19.  What  is  the  interest  of  $100  for  60  days  ? 
Solution.  The  interest  of  $1  for  60  days  is  1  cent  ;, 

therefore  the  interest  of  $100  is  100  cents,  or  $1. 

20.  What  is  the  interest  of  $30  for  60  (Jays  ?     For 
SO  days  ?   20  days  ?   40  days  ? 

21.  What  is  the  interest  of  $40  for  60  days?    For 
30  days  ?   15  days  ?   45  days  ?   75  days  ? 

22.  What  is  the  interest  of  $20  for  33  days 
Suggestion.  33  days  =  30  days  -f-  -fa  of  30  days. 

23.  What  is  the  interest  of  $40  for  33  days  ?    For 
66  days  ?    90  days  ?   93  days  ? 


LES.  III.]  AEITHMETIC.  145 

24.  The  interest  of  any  sum  of  money  for  1  year,  at 
5  per  cent.,  is  what  part  of  the  principal  ? 

Solution.  5  per  cent,  is  Tthr=2V>  therefore,  the 
interest  of  any  sum  for  1  year  at  5  per  cent,  is  ^o  °f 
the  principal, 

25.  What  is  the  interest  of  $40  for  1  year  at  5  per 
cent.  ? 

26.  At  4  per  cent.,  the  interest  of  any  sum  for  1 
year  equals  what  part  of  the  principal  ? 

27.  At  10  per  cent.,  the  interest  equals  what  part 
of  the  principal  ?   At  12|  per  cent.  ?   At  20  per  cent.  ? 
At  16|  per  cent.  ? 

28.  What  is  the  interest  of  $24  for  1  year  at  16| 
per  cent.  ?     At  12£  per  cent.  ?     At  25  per  cent.  ? 

29.  What  is  the  interest  of  $75  for  1  year  at  4  per 
cent.  ?     At  8  per  cent.  ?     At  33  J  per  cent.  ? 

30.  What  is  the  interest  of  $60  for  1  year  and  6 
months  at  5  per  cent.  ? 

31.  What  is  the  interest  of  $32  for  1  year  and  6 
months  at  12  J  per  cent.  ? 

32.  At  6J  per  cent.,  what  is  the  interest  of  $32  for 

1  year  ?     For  2  years  ?     1  year  and  6  months  ? 

33.  At  8J-  per  cent.,  what  is  the  interest  of  $72  for 

2  years  ?     For  1  year  and  6  months  ? 

LESSON  IIL 

1.  WHAT  is  the  amount  of  $50  for  1  year? 
Solution.  The  interest  of  $50   for   1   year  is  $3  ; 

therefore,  the  amount  is  $50  -|-  $3  =  $53. 

2.  What  is  the  interest  of  $200  for  2  years  and  6 
months  ?     What  the  amount  ? 

3.  What  is  the  amount  of  $60  for  60  days  ? 

4.  What  is  the  amount  of  $80  for  33  days  ? 

5.  What  is  the  amount  of  $84  for  90  days  ? 

6.  What  is  the  amount  of  $50,  at  4  per  cent.,  for 
2  years  and  6  months  ? 

10 


146  INTELLECTUAL  [SEC.  VIII. 

7.  What  is  the  amount  of  $60,  at  8J  per  cent.,  for 
3  years  and  3  months  ? 

8.  What  is  the  amount  of  $64,  at  12J  per  cent., 
for  2  years  and  9  months  ? 

9.  What  is  the  amount  of  $36,  at  16§  per  cent., 
for  2  years  and  3  months  ? 

10.  What  is  the  amount  of  $84,  at  25  per  cent.,  for 
2  years  and  6  months  ? 

11.  At  what  rate  per  cent,  will  $6  gain  45  cents  in- 
terest in  1 J  years  ? 

Solution.  The  interest  of  $6  for  1  year,  at  1  per  cent., 
is  6  cents,  and  for  1£  years  it  is  1^  times  6  cents,  or 
9  cents.  If  $6,  at  1  per  cent.,  gains  9  cents,  then  to 
gain  45  cents  will  require  as  many  per  cent,  as  9  cents 
is  contained  times  in  45  cents :  9  cents  in  45  cents,  5 
times ;  therefore,  $6,  at  5  per  cent.,  will  gain  45  cents 
in  1^  years. 

Or,  thus :  Since  the  interest  for  1  £  years  or  f  years 
is  45  cents,  for  ^  year  it  is  ^  of  45  cents,  or  15  cents, 
and  for  f  years  or  a  whole  year  it  is  2  times  15  cents, 
or  30  cents  ;  30  cents  is  -gfa  =  i'%i5  °f  $6 ;  T$^  is  5  per 
cent. ;  therefore,  $6,  at  5  per  cent.,  gains  45  cents  in  1^ 
years. 

12.  At  what  rate  per  cent,  will  $8  gain  96  cents 
in  1  year  and  6  months ;  that  is,  in  1  \  years  ? 

1 3.  At  what  per  cent,  will  $1 00  gain  $1 0^-  in  1 J  years  ? 

14.  At  what  per  cent,  will  $50  gain  $10  in  2  years  ? 

15.  At  what  per  cent,  will  $12  gain  80  cents  in  1 
year  and  4  months  ? 

1 6.  At  what  per  cent,  will  a  given  principal  double 
itself  in  20  years  ? 

Solution.  Any  principal  will  double  itself  in  1  year, 
at  100  per  cent. ;  and,  therefore,  in  20  years,  at  ^  of 
100  per  cent.,  viz.,  5  per  cent. 

17.  At  what  per  cent,  will  any  principal  double  it- 
self in  25  years?     In  10   years?     12 J  years  ?     50 
years  ?    16f  years  ?    33  J  years  ?    5  years  ?   4  years  ? 


Lts.  IV.]  AIUTHMETIC.  147 

18.  In  what  time  will  $6,  on  interest  at  5  per  cent., 
gain  70  cents  ? 

Solution.  $6,  at  5  per  cent.,  gains  30  cents  in  1 
year ;  30  cents  in  70  cents,  2^  times  ;  therefore,  $6,  at 
5  per  cent.,  will  gain  70  cents  in  2J  years,  or  2  years 
and  4  months. 

19.  In  what  time,  at  6  per  cent.,  will  $10  gain  $3  ? 

20.  In  what  time,  at  10  per.cent.,  will  $100  gain  $25  ? 

21.  In  what  time,  at  4  per  cent,  will  $4  gain  24 
cents  ? 

22.  In  what  time,  at  8  per  cent.,  will  $50  gain  $23  ? 

23.  In  what  time,  at  5  per  cent.,  will  a  given  prin- 
cipal double  itself? 

/Solution.  Any  principal,  at  1  per  cent.,  will  double 
itself,  i.  e.  it  will  gain  100  per  cent.,  in  100  years ; 
and  at  5  per  cent.,  in  £  of  100  yearsy  viz.,  20  years. 

24.  In  what  time,  at  4  per  cent.,  will  any  principal 
double  itself?     In  what  time,  at  6  per  cent.  ?   At  8 
per  cent.  ?     At  20  per  cent.  ?     At  25  per  cent.  ?     At 
2  per  cent.?     At  50  per  cent.?     At*  12 J  per  cent.? 
At  6£  per  cent.  ?  At  16f  per  cent.  ?  At  33 £  per  cent.  ? 

LESSON  IV. 

1.  WHAT  principal,  at  6  per   cent.,  will   gain  36 
cents  in  1  year  and  6  months  ? 

Solution.  $1,  at  6  per  cent.,  gains  9  cents  in  1  year 
and  G^months  ;  9  cents  in  36  cents,  4  times;  therefore, 
$4,  at  6  per  cent.,  will  gain  36  cents  in  1  year  and  6 
months. 

Or,  since  the  interest  of  any  sum  for  1  year  and  6 
months,  at  6  per  cent.,  is  y^  of  the  principal,  it  fol- 
lows that  36  cents  is  T§<y  of  the  required  principal ; 
hence,  ^  of  36  cents,  or  4  cents,  is  T^,  and  yg|  is  100 
times  4  cents,  which  is  400  cents,  or  $4  ;  therefore,  etc. 

2.  What  principal,  at  5  per  cent.,  will  gain  60  cents 
in  2  years  ? 


143  INTELLECTUAL  [SEC.  VIII. 

3.  What  principal,  at  8  per  cent.,  will  gain  $2  in  G 
months  ? 

4.  What  principal,  at  10  per  cent.,  will  gain  $15  in 
1  year? 

5.  What  principal,  at  8  per  cent.,  will  gain  $60  in 
3  years  and  9  months  ? 

6.  What  principal,  at  10  per  cent,,  will  amount  to 
$6.60  in  1  year  ? 

Solution.  The  amount  of  $1  for  1  year,  at  10  per 
cent.,  is  $1.10  ;  $1.10  in  $6.60,  6  times  ;  therefore, 
$6,  at  10  per  cent.,  will  amount  to  $6.60  in  1  year. 

Or,  the  interest  of  any  sum  for  1  year,  at  10  per 
cent.,  is  -j^  of  the  principal,  and  this  added  to  the 
principal,  -}-$,  makes  the  amount  =  -J-i  of  the  principal ; 
hence,  $6.60  is  |J  of  the  principal,  and'^  of  $6.60,  or 
60  cents,  is  -fa,  and  |g,  or  the  whole  principal,  is  10 
times  60  cents  =  600  cents,  or  $6 ;  therefore,  etc. 

7.  What  principal,  at  5  per  cent.,  will  amount  to 
$22  in  2  years  ?     To  $44  in  2  years  ? 

8.  What  principal,  at  8  per  cent,,  will  amount  to 
}  in  2  years  ?     To  $84  in  1 J  years  ? 

9.  What  principal,  at  4  per  cent.,  will  amount  to 
$66  in  5  years  ?     To  $280  in  10  years  ? 

10.  What  principal,  at  12  J  per  cent.,  will  amount 
to  $250  in  2  years?     To  $121  in  3  years  ? 

11.  What  principal,  at  16f  percent.,  will  amount 
to  $42  in  1  year  ?     To  $80  in  2  years  ? 

12.  What  principal,  at  6  per  cent.,  will  amount  to 
$10.60   in   1   year?     To  $21.80   in    1  year  and   6 
months  ? 

13.  What  sum  can  I  obtain  at  a  bank  for  a  note  of 
$80,  payable  -in  60  days  ? 

Solution.  The  interest  of  $80  for  60  days  is  80  cents, 
which,  taken  from  $80,  leaves  $79.20 ;  therefore,  etc. 

14.  What  sum  can  I  obtain  at  a  bank  for  a  note  of 
$48,  payable  in  45  days  ?     What  sum  for  a  note  of 
$64,  payable  in  75  days  ? 


LES.  I.]  ARITHMETIC.  149 

SECTION  NINTH. 
LESSON  I. 

1.  BOUGHT  21b.  of  figs,  at  20  cents  per  pound, 
and  gave  in  payment  a  quarter  of  a  dollar,  a  dime, 
and  the  rest  in  cents ;  how  many  cents  did  I  give  ? 

2.  I  have  a  rectangular  field  20  rods  long  and  15 
rods  wide  ;  what  will  it  cost  to  build  a  wall  around  it, 
at  $1.50  a  rod? 

3.  I  have  a  field  containing  3  roods  and  10  rods  ; 
what  is  it  worth,  at  $2  per  square  rod  ? 

4.  What   is   the  cost   of  a  load   of  wood  which 
measures  1  cord  and  2  cord  feet,  at  75  cents  per  cord 
foot? 

5.  How  many  days  from  July  4th,  at  9  o'clock  in 
the  morning,  to  Aug.  10th,  at  9  o'clock  in  the  evening  ? 

6.  What  cost  3  score  bushels  of  corn,  at  J  of  a 
dollar  a  bushel  ? 

7.  If  a  ship  sail  180  miles  each  day,  how  far  does 
she  sail  in  a  week  ? 

8.  Bought  a  load  of  wood  which  measured  9  cord 
feet ;  f  of  the  load  was  pine,  at  $4  a  cord,  and  the  rest 
was  oak,  at  75  cents  a  cord  foot ;  what  was  the  cost 
of  the  load  ? 

9.  What  cost  10  J  acres  of  land,  at  $20  per  acre  ? 

10.  I   have  a  sauars   piece  of  land  each  side  of 
which  is  3C  .eet  long ;  how  many  rods  is  it  round  this 
piece  ? 

11.  If  it  takes  16^  yards  of  silk  to  make  a  dress, 
what  will  the  silk  for  2  dresses  cost,  at  1^  dollars  per 
yard  ? 

12.  I  have  a  rectangular  garden  which  is  12  rods 
long  and  7  rods  wide ;  how  many  square  rods  does  it 
contain  ? 

13.  Mr.  Smith  has   a  rectangular  garden,    6  rods 
wide,  and  containing  48  square  rods  ;  how  long  is  it  ? 


150  INTELLECTUAL  [SEC.  IX. 

14.  Mr.  French  has  a  rectangular  garden  10  rods 
long  and  containing  70  square  rods ;.  how  wide  is  it  ? 

15.  A  man  bought-  a  share  of  the  Boston  and  Maine 
Railroad  stock  for  $100,  and  sold  it  for  $103  ;  what 
per  cent,  on  the  purchase  money  did  he  gain  ? 

1 6.  A  grocer  bought  a  box  of  sugar  for  $12,  and  sold 
it  so  as  to  gain  5  per  cent. ;  how  much  did  he  gain  ? 

17.  A  merchant  bought  a  piece  of  silk  for  $75,  and 
sold  it  so  as  to  gain  10  per  cent. ;  how  much  did  he 
gain  ?     What  did  he  receive  for  the  silk  ? 

18.  A  shoedealer  bought  boots  at  $4  a  pair,  and 
sold  them  at  §5 ;  what  per  cent,  did  he  gain  ?     He 
bought  others  at  $5,  and  sold  them  at  $4 ;  what  per 
cent,  did  he  lose  ? 

19.  A  grocer  bought  molasses  at  40c.  per  gallon; 
how  shall  he  sell  it  to  gain  25  prr  cent.  ? 

20.  A  merchant  bought  goods  for  $50,  but,  they 
being  damaged,  he  is  willing  to  lose  20   per  cent. ; 
for  what  sum  is  he  willing  to  sell  them  ? 

21..  A  laborer  agreed  to  work  5  months  for  60  dol- 
lars; how  much  did  he  receive  for  a  month?  How 
much  for  a  week,  allowing  4  weeks  to  the  month  ? 
How  many  shillings  a  day,  allowing  6  working-days  to 
the  week  ? 

22.  If  a  melon  is  worth  8  oranges,  how  many  melons 
are  44  oranges  worth  ? 

23.  A  man  sold  24  hens  al  *he  rate  of  3  for  a  dollar  ; 
how  many  dollars  did  he  receive  ? 

24.  If  wine  is  worth  24  cents  a  pint,  what  is  1  gill 
worth  ?     What  are  3  gills  worth  ? 

25.  At  80  cents  a  bushel,  what  is  a  peck  of  corn 
worth  ?     What  is  a  half  peck  worth  ? 

26.  Five  boys  bought  a  sled  for  90  cents,  and  sold  it 
for  75  cents  ;  sharing  the  loss  equally,  what  did  each 
boy  lose  by  the  bargains  ? 

27.  A  man  paid  $35  for  wood,  at  $7  a  cord  ;  how 
many  cords  did  he  buy  ? 


LES.  L]  ARITHMETIC.  151 

28.  A  man  paid  $63  for  9  cords  of  wood ;  what  was 
the  price  per  cord  ? 

29.  A  hound  is  36  rods  behind  a  fox,  and  both  are 
running  in  the  same  direction  ;  but  the  hound  gains 
upon  the  fox  3  rods  in  a  minute ;  in  how  many  min- 
utes will  the  hound  overtake  the  fox  ? 

30.  A  fox  is  48  rods  from  a  hound,  and  running  80 
rods  per  minute ;  but  the  hound  is  pursuing  him  at  the 
rate  of  83  rods  per  minute  ;  how  many  minutes  can 
the  fox  run  before  tke  hound  overtakes  him  ? 

31.  What  will  9  quarts  of  milk  cost,  if  6  quarts 
cost  24  cents  ? 

32.  A  cask  containing  56  gallons,  has  a  pipe  which 
discharges  8  gallons  per  minute ;  in  how  many  min- 
utes will  the  cask  be  emptied  ? 

33.  There  is  an  empty  cask  that  will  hold  84  gallons, 
and,  by  a  pipe,  12  gallons  run  into  it  in  a  minute ;  in 
how  many  minutes  will  the  cask  be  filled  ? 

34  An  empty  cask,  that  will  hold  48  gallons,  receives 
10  gallons  per  minute  by  one  pipe,  and  discharges  6 
gallons  per  minute  by  another  pipe ;  how  many  gal- 
lons remain  in  the  cask  in  one  minute  ?  In  what 
time  will  the  cask  be  filled  ? 

35.  A  vessel  which  contains  63  gallons  of  water,  dis- 
charges 12  gallons  per  minute  by  one  pipe,  and  re- 
ceives 9  gallons  per  minute  by  another  pipe ;  in  how 
many  minutes  will  the  vessel  be  emptied  ? 

3  6.  "If  1  man  can  do  a  piece  of  work  in  42  days,  in 
how  many  days  can  7  men  do  it  ?  In  how  many 
days  can  1 2  men  do  it  ? 

37.  If  1  man  can  do  a  piece  of  work  in  55  days, 
how  many  men  can  do  the  same  in  5  days  ? 

38.  A  man  can  do  a  piece  of  work  in  66  hours ;  in 
how  many  days  can  he  do  it  if  he  works   11  hours 
each  day  ? 

39.  A  man  can  do  a  certain  job  in  56  hours ;  how 
many  hours  a  day  must  he  work  to  do  it  in  7  days  ? 


152  INTELLECTUAL  [SEC.  IX. 

40.  If  you  wish  to  put  72  pounds  of  butter  into  6 
boxes,  bow  many  pounds  will  you  put  into  each  box  ? 

41.  If  you  put  84  pounds  of  butter  into  boxes  that 
will  hold  7  pounds  apiece,  how  many  boxes  will  it  take  ? 

42.  A  farmer  bought  9  yards  of  cloth,  at  $4  a  yard, 
and  paid  for  it  with  apples,  at  $3  a  barrel ;  how  many 
barrels  did  it  take  ? 

43.  Two  boys  are  45  rods  apart,  and  both  running 
in  the  same  direction ;   the  hindmost  boy  gains  on  the 
other  5  rods  in  a  minute;- in  how  many  minutes  will 
he  overtake  him  ? 

44.  A  grocer  bought  5  firkins  of  butter  for  $50, 
and  sold  them  so  as  to  gain  $10  ;  what  did  he  pay  for 
each  firkin  ?    What  did  he  gain  on  each  ?     What  did 
he  receive  for  each  ? 

45.  How  many  yards  of  cloth,  at  $5  a  yard,  may 
be  bought  for  10  reams  of  paper,  at  $2  a  ream  ? 

LESSON  II. 

1.  WHAT  number  added  to  twice  itself  gives  15  ? 
Solution.  Any  number  plus  twice  the  same  number 

is  3  times  that  number;  therefore,  15  is  3  times  the 
required  number,  and  ^  of  15,  viz.,  5,  is  the  number. 

2.  What  number  added  to  3  times  itself  gives  32  ? 

3.  William  and  George  together  caught  35  fishes, 
.and  William  caught  3  as  often  as  George  caught  2  ; 
how  many  did  each  boy  catch  ? 

4.  Two  times  a  certain  number,  added  to  3  times 
the  same  number,  make  35  ;  what  is  the  number  ? 

5.  A  boy  gave  35  nuts  to  two  of  his  companions, 
giving  4  nuts  to  one  of  them  as  often  as  he  gave  3  to 
the  other ;  how  many  did  he  give  to  each  ? 

6.  What  number  added  to  £  of  itself  gives  15  ? 

7.  A  boy  being  asked  how  old  he  was,  replied,  I 
am  half  as  old  as  my  sister,  and  the  sum  of  our  ages  is 
27  years  ;  how  old  was  he  ? 


LES.  II.]  ARITHMETIC.  153 

8.  A  father  gave  64  cents  to  his  two  sons,  giving  J 
as  many  to  the  younger  as  to  the  older ;  how  many 
cents  did  he  give  to  each  ? 

9.  A  boy  divided  28  peaches  among  3  of  his  corn* 
panions,  giving  twice  as  many  to  the  first  as  to  the 
second,  and  twice  as  many  to  the  second  as  to  the  third  ; 
how  many  did  he  give  to  each  ? 

10.  A  boy  gave  42  peaches  to  3  of 'his  companions, 
giving  half  as  many  to  the  first  as  to  the  second,  and 
half  as  many  to  the  second  as- to  the  third;  how  many 
did  he  give  to  each  ? 

11.  A  and  B  together  have  45  marbles,  and  A  has 
J  as  many  as  B  ;  how  many  has  each  ? 

12.  A  man  being  asked  how  many  sheep  he  had, 
replied  that  if  he  had  what  he  then  had,  and  ^  and  £ 
as  many  more,  he  should  have  55  ;  how  many  had  he  ? 

13.  A  boy  having  48  apples,  kept  4  of  them  himself 
and  gave  the  rest  to   Reuben,  David,  and  Samuel, 
giving  ^  as  many  to  .David  and  ^  as  many  to  Samuel 
as  to  Reuben  ;  how  many  did  he  give  to  Reuben  ? 

14.  A  merchant  bought  a  piece  of  cloth,  at  $6  a 
yard,  and  another  piece  of  the  same  length,  at  $2  a 
yard,  and  afterward  sold  the  .whole,  at  $4  a  yard ;  did 
he  either  gain  or  lose  by  the  transactions  ? 

15.  A  fruiterer   employed   two   boys,    Frank   and 
Arthur,  to  sell  apples  for  him.     The  dealer  intrusted 
60  apples-  to  each  boy,  and  told  him  he  might  sell  them 
at  the  rate  of  5  apples  for  2  cents,  and  Frank  sold  his 
as  instructed ;  but  Arthur  thought  he  might  sell  his 
more  readily  if  he  sorted   them   according  to   their 
quality ;  so  he  separated  them,  putting  30  apples  into 
one  part  of  his  basket,  and  the  other  30  into  another 
part.     He  sold  the  better  lot  at  the  rate  of  2  apples 
for  1  cent,  and  the  poorer  lot  at  the  rate  of  3  for  1 
cent.     Now,  did  the  two  boys  receive  equal  sums  for 
their  entire  stock  of  apples  ?     If  not,  which  was  the 
more  profitable  to  his  employer  ?     How  much  ? 


154  INTELLECTUAL  [SEC.  IX. 

16.  A  boy  was  asked  how  many  chickens  he  had, 
when  he  replied  that  if  he  had  as  many  more,  and  ^ 
and  -J-  as  many  more  and  2  chickens,  he  should  have 
70  ;  how  many  had  he  ? 

17.  A  boy  being  asked  his  age,  said  that  if  J  and  £ 
of  his  age  and  10  years  more  were  added  to  his  age, 
the  sum  would  be  3  times  his  age ;  how  old  was  he  ? 

18.  A  pole  48  feet  long  has  one  third  as  much  in 
the  mud  as  in  the  water,  and  twice  as  much  in  the  air 
as  in  the  mud  and  water  together ;  how  many  feet 
WQre  there  in  the  water  ? 

1!).  Suppose  that  A  lends  money  at  6  per  cent.,  in- 
terest payable  in  bank  bills,  and  that  B  buys  6  per 
cent,  government  bonds,  at  20  per  cent,  premium, 
which  makes  the  best  investment  if  the  bonds  are  pay- 
able in  paper  in  20  years  and  the  interest  on  the  bonds 
payable  in  gold  annually,  gold  being  at  50  per  cent, 
premium  ?  Why  ? 

20.  Which  is  the  more  profitable,  to  lend  money  at 
6  per  cent.,  or  to  buy  5  per  cent,  government  bonds, 
at  10  per  cent,  premium,  the  other  conditions  being 
the  same  as  in  example  19  ? 


LESSON  HI. 

1.  DIVIDE  32  into  two  such  parts  that  the  less  part 
shall  have  the  same  relation  to  the  greater  that  3  has 
to  5. 

Solution.  3  and  5  are  8 ;  therefore,  if  32  is  divided 
into  8  equal  parts,  3  of  those  parts  will  be  "the  less  of 
the  two  required  numbers,  and  5  of  them  will  be  the 
greater.  3  times  \  of  32  are  12,  the  less  part,  and  5 
times  £  of  32  are  20,  the  greater  part. 

NOTE.  This  is  usually  called  Ratio.  The  ratio  of  3  to  5  is 
J,  and  the  ratio  of  12  to  20  is  J£,  which  can  be  reduced  to  3. 

2.  Two  boys  bought  a  melon  for  40  cents,  and  cut 


LES.  Ill]  ARITHMETIC.  155 

it  into  5  equal  parts.     One  boy  took  3  ot  the  parts, 
and  the  other  took  2  ;  what  ought  each  to  pay  ? 

3.  Two  men  hire  a  pasture  for  $60.  One  man  keeps 
5  cows  in  the  pasture  through  the  summer,  and  the 
other  keeps  7  ;  how  much  ought  each  to  pay  ? 

4.  Two  boys  engage  to  cut  a  pile  of  wood  for  $33. 
One  boy  cuts  6  cords  while  the  other  cuts  5  ;  how 
should  the  pay  be  divided  ? 

5.  Two    men    engage    in   trade.     One    furnishes 
$7000  and  the  other  $5000,  and  in  a  year  they  gain 
$2400  ;  how  should  the  profits  be  divided? 

6.  A,  B,  and  C  hire  a  pasture  for  $100.     A  pas- 
tures 3  cows,  B  8,  and  C  9 ;  how  many  dollars  ought 
each  to  pay  ? 

7.  David,  Samuel,  and  John  buy  80  marbles  for  20 
cents ;  David  takes  1  marble  as  often  as  Samuel  takes 
4,  and  John  5 ;  how  many  does  each  take  ?     What 
shall  each  pay  ? 

8.  A  and  B  trade  in  company,  furnishing  money 
in  the  ratio  of  §4  to  $5.     They  gain  $2700  ;  what  is 
the  share  of  each  ? 

9.  Two  travelers,  54   miles  apart,  approach  each 
other,  one  at  the  rate  of  4  miles  an  hour,  and  the  other 
at  the  rate  of  5  miles  an  hour ;  how  far  will  each  travel 
before  they  meet  ? 

10.  A  gentleman  gave  28  pears  to  some  children  ;  to 
each  girl  4,  and  to  each  boy  3.     There  were  as  many 
boys  as  girls  ;  how  many  pears  did  he  give  to  all  the 
boys  ?     To  all  the  girls  ? 

11.  Sarah  had  12  cents,  and  Nancy  had  18  cents; 
they  paid  all  their  money  for  10  oranges;  how  many 
oranges  ought  each  to  receive  ? 

12.  A,  B,  and  C  traded  in  company.      A   put    in 
$2  as  often  as  B  put  in  $3,  and  as  often  as  C  put  in 
$4.     They  gained  $63 ;  what  was  the  share  of  each  ? 

13.  A  man  failing  in  business,  has  property  valued 
at  $900  ;  but  he  owes  to  A  $300,  to  B  $400,  and  to  C 


ir>G  INTELLECTUAL  [SEC.  IX. 

$~>00  ;  what  part  of  his  debts  can  he  pay  ?  How  many 
dollars  to  each  creditor  ? 

14.  Addie  and  Georgie  together  solved  60  exam- 
ples, and  Addie  solved  %  as  many  as  Georgie  ;  how 
many  did  each  solve? 

\'t.  The  sum  of  the  ages  of. William  and  James  is 
:>r>  years,  and  James  ig  £  as  old  as  William  5  what  is 
the  age,  of  each  ? 

1<>.  Divide  $24  between  A  and  B,  giving  to  A  $1 
as  often  as  J  of  a  dollar  to  B. 

17.  Edward   had   a  certain  number  of  cents,  and 
found  J  as  many  more,  when  he  had  32  cents  ;  how 
many  cents  will  he  have  left  after  spending  f  of  what 
he  found  ? 

18.  Three  men,  A,  B,  and  C,  traded  in  company. 
A  put  in  $2  as  often  as  B  -put  in  $3,  and  C  put  in 
such  a  sum  that  he  received.  $36  of  the  $66  gained  in 
the  year  ;  what  was  the  share  of  the  gain  received  by 
A  and  B,  and  how  many  dollars  did  C  furnish  as  often 
as  A  furnished  §2? 


LESSON  IV. 

1.  A  AND  B  traded  in  company.    A  put  in  $10  for 
2  months,  and  B.  put  in  $8  for  3  months.    They  gain 
$88  ;  what  is  each  one's  share  of  the  gain  ? 

Solution.  A's  $10  for  2  months  are  the  same  as 
$20  for  1  month,  and  B's  8  for  3  months  are  the  same  as 
$24  for  1  month  ;  therefore,  the  total  capital  may  be 
considered  $44,  and  A's  share  is  ff  or^\?  an(l  B's 
share  is  f  f  or  T\ ;  y\  of  $88  is  $40,  A's  share  of  the 
gain,  and  T6T  of  $88  is  $48,  B's  share. 

2.  A  and  B  hire  a  pasture  for  $11.    A  pastures 
2  horses  for  5  weeks,  and  B  pastures  3  horses  for  4 
weeks  ;  what  is  each  one's  share  of  the  expense  ? 

3.  Two  men,  A  and  B,  hire  a  pasture  for  $10,  and 
agree  that  2  cows  shall  be  reckoned  as  I  horse.    A 


LES.  IV.]  ARITHMETIC.  157 

pastures  2  horses  and  4  cows  for  3  weeks,  and  B  pas- 
tures 3  horses  and  2  cows  for  2  weeks  ;  how  many 
dollars  shall  each  pay  ? 

4.  A,  B,  and  C  traded  in  company.    A  put  in  $2  as 
often  as  B  put  in  $3,  and  as  often  as  C  put  in  $5.    'B's 
money  was  in  twice  as  long  as  C's,  and  A's  twice  as 
long  as  B's.     They  gained  $38  ;  what  was  each  one's 
share  of  the  gain  ? 

5.  A  and  B  trade  in  company.     A  puts  in  $10  for 
2  months,  and  B  puts  in  $9  for  3  months.     They  lose 
$94;  what  is  the  loss  of  each? 

6.  A  and  B  cut  a  field  of  grain  for  $42.    A  works 
12  days,  and  B  works  6  days.     What  sum  should  each 
receive,  if  B  can  do  as  much  in  2'  days  as  A  can  do  in  3 
days  ?  How  much  does  A  earn  per  day?  How  much  B  ? 

7.  Two  men,  A  and-  B,  agree  to  do  a  piece  of  work 
for  $88.     A  employs  3  men  4  days,  and  B  employs  5 
men  2  days  ;  what  part  of  the  pay  shall  each  have  ? 
How  many  dollars  ? 

8.  A  man  divided  $40  between  his  4  sons  and  3 
daughters,  giving  each  son  J  as  much  as  each  daugh- 
ter ;  what  was  the  share  of  each  ? 

9.  Divide  15  peaches  between  B  and  C,  so  that  B 
may  have  3  peaches  more  than  C. 

10.  The  sum  of  2  numbers  is  21,  and  the  greater 
exceeds  the  less  by  5  ;  what  are  the  numbers  ? 

11.  A  and  B  together  have  40  cents,  and  A. has 
10  cents  less  than  B  ;  how  many  cents  has  each  ? 

12.  David   bought  twice  as  many  pears  as  John, 
and  after  David  had  eaten  6  and  John  4,  they  together 
had  26 ;  how  many  pears  had  each  remaining? 

13.  If  2  melons  are  worth  12  oranges,  and  8  or- 
anges are  worth  24  apples,  how  many  apples  shall  I 
give  for  3  melons  ? 

14.  If  2  oxen  are  worth  3  cows,  and  4  cows  are 
worth  24  sheep,  what  is  1  ox  worth,  supposing  a  sheep 
to  be  worth  $7  ? 


153  INTELLECTUAL  [SEC.  IX. 

15.  A  hare  is  7  of  his  own  leaps  before  a  hound, 
and  takes  5  leaps  while  the  hound  takes  3,  but  4  of 
the  hound's  leaps  are  equal  to  7  of  the  hare's  ;  how 
many  leaps  must  the  hound  take  to  gain  on  the  hare 
the  length  of  one  of  the  hare's  leaps  ?     How  many 
leaps  must  the  hound  take  to  catch  the  hare  ? 

Solution.  Since  1  of  the  hound's  leaps  is  J  of  a  leap 
of  the  hare,  3  of  the  hound's  leaps  are  equal  to  ^-,  or 
5£  of  the  hare's  leaps  ;  hence,  in  taking  3  leaps  the 
hound  gains  ^  of  one  leap  of  the  hare,  and  therefore  he 
must  take  4  times  3  leaps,  or  12  leaps,  to  gain  1  leap 
of  the  hare ;  and  to  gain  7  leaps,  he  must  take  7  times 
12  leaps,  or  84  leaps. 

16.  Charlie  is  10  of  his  own  steps  before  John,  and 
takes  6  steps  while  John  takes  5,  but  3  of  John's  steps 
are  equal  to  4  of  Charlie's;  how  many  steps    must 
John  take  to  gain  the  length  of  one  of  Charlie's  step*  ? 
How  many  steps  can  Charlie  take  before  John  will 
catch  him  ? 

17.  A  lady  wishing  to  buy  a  certain  number  of 
yards  of  silk  for  a  dress,  finds  that  if  she  pays  a  dollar 
a  yard  she  will  have  5  dollars  left ;  but  if  she  pays  a 
dollar  and  a  half  per  yard,  she  must  get  trusted  for  2 
dollars  ;  how  many  yards  does  she  wish  to  buy  ? 

18.  A  man  and  his  wife  would  eat  a  sack  of  flour 
in  15  days,  and  after  living  together  for  6  days  the 
woman  alone  would  consume  the  remainder  in  24  days ; 
how  many  days  would  the  whole  sack  last  the  woman  ? 
How  many  days  the  man  ? 

19.  A  boy  being  asked  how  many  hens -he  had,  said 
that  if  he  had  half  as  many  more  and  four  hens  and  a 
half,  he  should  have  3  dozen  ;  how  many  hens  had  he  ? 

20.  A  farmer,  questioned  with  regard  to  the  num- 
ber of  his  sheep,  said  that  if  he  had  as  many  more, 
half  as  many  more,  and  2  sheep  and  a  half,  he  should 
have  100  ;  how  many  had  he  ? 

21.  A  boy  engaged  to  live  with  a  man  30  (lays,  agree- 


LES.  IV.]  ARITHMETIC.  159 

ing  to  receive  3  shillings  a  day  for  every  day  he 
worked,  and  to  pay  2  shillings  a  day  for  his  board 
every  day  he  played.  At  the  end  of  the  30  days  he 
received  60  shillings  ;  how  many  days  did  he  work  ? 

22.  A  fish's  head  weighs  5  pounds,  his  tail  weighs 
as  much  as  his  head  added  to  half  the  weight  of  his 
body,  and  his  body  weighs  as  much  as  his  head  and 
tail  together  ;  what  is  the  weight  of  the  fish  ? 

23.  A  and  B  start  from  towns  which  are  48  rniles 
apart,  and  travel  toward  each  other  until  they  meet, 
when  it  appears  that  ^  of  the  distance  A  has  traveled 
is  equal  to  f  of  the  distance  B  has  traveled ;  how  far 
has  each  traveled  ? 

24.  A  purse  and  its  contents  are  worth  41  shillings, 
and  f  of  the  value  of  the  purse  are  equal  to  f  of  the 
value  of  the  contents  ;  what  is  the  value  of  the  purse  ? 

25.  Seven  times  a  certain  number  is  15  more  than 
4  times  the  same  number  ;  what  is  the  number ; 

26.  What  number  is  that  to  which  if  its  half  and  its 
fourth  be  added,  the  sum  will  be  35  ? 

27.  What  sum  of  money  can  I  obtain  at  a  bank  for 
a  note  of  S3  6,  payable  in  90  days  ? 

28.  If  a  5  cent  loaf  weighs  24  ounces  when  flour  is 
worth  $6  per  barrel,  what  ought  it  to  weigh  when 
flour  is  worth  $9  per  barrel  ? 

29.  A  man  failing  in  business,  is  able  to  pay  only 
80  per  cent,  of  his  debts  ;  how  much  will  he  pay  on  a 
debt  of  $30? 

30.  Bought  8  A  lb.  of  honey  at  one  time,  3^  lb.  at 
another    time,    10|£  lb.    at   another,    and   6JJ  lb.    at 
another ;  how  many  pounds  did  I  buy  at  the  four  times  ? 

31.  A,  B,  and  C  can  do  a  certain  piece  of  work  in 
4  days.     A  can  do  ^  of  it  in  1  day,  and  B  can  do  ^  of 
it  in  1  day;  in  how  man}Tdays  can  C  do  the  whole  work  ? 

32.  A  gentleman  being  asked  the  time  of  day,  re- 
plied that  §  of  the  time  past  from  noon  was  equal  to  f 
of  the  time  to  come  before  midnight;  what  was  the  time  ? 


1GO 


MULTIPLICATION   TABLE. 


Ouce 

Twice 

3  times 

4  times 

5  time* 

6  times 

1  is  1 

1  are  2 

1  are  3 

1  are  4 

1  are  5 

1  are  6 

2     2 

2     4 

2     6 

2     8 

2    10 

2    12 

3     3 

3     6 

3     9 

3    12 

3    15 

3    18 

4     4 

4     8 

4    12 

4    16 

4    20 

4    24 

5     5 

5    10 

5    15 

5    20 

5    25 

5    30 

6     6 

6    12 

6    18 

6    24 

6    30 

6    36 

7     7 

7    14 

7    21 

7    28 

7    35 

7    42 

8     8 

8    16 

8    24 

8    32 

8    40 

8    48 

9     9 

9    IS 

9    27 

9    36 

9    45 

9    54 

10    10 

10    20 

m   so 

10    40 

10    50 

10    60 

11    11 

11    22  11    33 

11    44 

11    55 

11    66 

12    12 

12    21 

12    36 

12    48 

12    60 

12    72 

7  times 

8  times 

9  times 

1O  times 

11  times 

1£  times 

1  are  7 

1  are  8 

1  arc  9 

1  are  10 

1  are  11 

1  are  12 

2    14 

2    16 

2    18 

2    20 

2    22 

2    24 

3    21  1  3    24 

3    27 

3    30 

3    33 

3    30 

4    28'  4    32 

4    36 

4    40 

4    44 

4    48 

5    35.  5    40 

5    45 

5    50 

5    55 

3    60 

6    42:  6    48 

6    54 

6    60 

6    60 

6    72 

7    49!  7    56 

7    63 

7    70 

7  '   77 

7    81 

8    56  8    64 

8    72 

8    80 

8    88 

8    00 

y    03  y    72 

9    81 

9    90 

9    99 

0    108 

10    7010    80 

10    90 

10   100 

10   110 

10    1:20 

11    77  11    88 

11    99 

11    110 

11    121 

li    \'1'2 

12    81 

12    96 

12   108 

12   120 

12    132  12    114 

1 

I 

13  times 

14  times 

15  times 

16  times 

17  times  I!N  times 

1  are  13 

1  are  14 

1  are  15 

1  are  16 

1  are  17  I  1  are  18 

2    26 

2    28 

2    30 

2    32 

2    34 

2    30 

3    39 

3    42 

3    45 

3    48 

3   /51 

3    54 

4    52 

4    56 

4    60 

4    64 

4    68 

4    72 

5    65 

5    70 

5    75 

5    80 

5    85 

5    90 

6    78 

6    84 

6    90 

6    96 

6   102 

6   10S 

7    91 

7    98 

7   105 

7   112 

7   119 

7    120 

8   104 

8   112 

8   120 

8   128  8   136 

S   14  1 

9   117 

9   126 

9   135 

9   144  9   153 

9    1  0  _' 

10   130 

10   140 

10   150 

10   100  10   170 

10    1*0 

11    143 

11    154 

11    165 

11    176  11    187  1  L    V.'S- 

12    156 

12   168 

12    180 

12    192  12    201  12    L'l'i 

, 

MULTIPLICATION  TABLE. 


161 


19  times 

2O  times 

31  times 

22  times 

23  times 

24  times 

laro  19 

1  arc  20 

1  are  21 

lare  22 

1  are  23 

1  are  24 

2    38 

2    40 

2    42 

2    44 

2    46 

2    48 

3    57 

3    60 

3    63 

3    66 

3    69 

3    72 

4    76 

4    80 

4    84 

4    88 

4    92 

4    96 

5    95 

5   100 

5   105 

5   110 

5   115 

5   120 

6   114 

6   120 

6   126 

6   132 

6   138 

6   144 

7   133 

7   140 

7   147 

7   154 

7   161 

7   168 

8   152 

8   160 

8   168 

8   176 

8   184 

8   192 

9   171 

9   180 

9   189 

9   198 

9   207 

9   216 

10   190 

10   200 

10   210 

10   220 

10   230 

10   240 

11   209 

11   220 

11   231 

11   242 

11   253 

11   264 

12   228 

12   240 

12   252 

12   264 

12   276 

12   288 

i3  times 

14  times 

15  times 

16  times 

17  times 

18  times 

13  are  169 

13  are  182 

13  are  195 

13  arc  208 

13  are  221 

13  are  234 

14   182 

14   196 

14   210 

14   224 

14   238 

14   252 

15   195 

15   210 

15   225 

15   240 

15   255 

15   270 

10   208 

16   224 

16   240 

16   256 

16   272 

16   288 

17   221 

17   238 

17   255 

17   272 

17   289 

17   306 

18   234 

18   252 

18   270 

18   288 

18   306 

18   324 

19   247 

19   266 

19   285 

19   304 

19   323 

19   342 

•20   260 

20   280 

20   300 

20   320 

20   340 

20   360 

•21   273 

21   294 

21   315 

21   336 

21   357 

21   378 

•22   286 

22   308 

22   330 

22   352 

22   374 

22   396 

•23   299 

23   322 

23   345 

23   S68 

23   391 

23   414 

•24   312 

24   336 

24   360 

24   384 

24   408 

24   432 

19  times 

2O  times 

21  times 

22  times 

23  time* 

24  times 

13  arc  247 

13  are  260 

13  are  273 

13  are  286 

13  are  299 

13  are  312 

14   266 

14   280 

14   294 

14   308 

14   322 

14   336 

15   285 

15   300 

15   315 

15   330 

15   345 

15   360 

16   304 

16   320 

16   336 

16   352 

16   368 

16   381 

17   323 

17   340 

17   357 

17   374 

17   391 

17   408 

18   342 

18   360 

18   378 

18   396 

18   414 

18   432 

19   361 

19   380 

19   399 

19   418 

19   437 

19   456 

20   380 

20   400 

20   420 

20   440 

20   460 

20   480 

21    399 

21   420 

21   441 

21   462 

21   483 

21   504 

22   418 

22   440 

22   462 

22   484 

22   506 

22   528 

437  23   460 

23   483 

23   506 

23   529 

23   552 

u.4   456  24   480 

24   504 

24   528 

24   552 

24   576 

11 


162 


REVIEW  TABLES. 


EXERCISES  IN  ADDITION. 


No.  1. 

4+3 
5+6 
6+4 
7+    7 
8+    6 

No.  2. 

5+5 
6+8 
4+    7 
7+    3 
8+5 

No.  3. 

6+    7 
5+    9 
8+    4 
12+3 
10+6 

No.  4. 

7+    8 
6  +  11 
5+    7 
4  +  12 
9+    6 

No.  5. 

8  +  11 
12+4 
10+  11 
5  +  12 
6+    5 

No.  6. 

6  +  12 
5+8 
7+    6 
8+9 
10+8 

No.  7. 

8+    7 
7+    9 
4+    4 
9+    3 
10+5 

No.  8. 

4+    5 
6  +  10 
5  +  11 
9+    7 
11  +  11 

No.  9. 

7  +  10 
4+    6 
5+3 
7  +  11 
"12+8 

No.  10. 

11+3 

4+    8 
7+    5 
12+6 
11  +  10 

No.  11. 

8+12 
11  +    7 
9+9 

7+    4 
8+8 

No.  12. 

10+4 
6+9 
7  +  12 
11+8 
4  +  10 

No.  13. 

12+5 
11+9 
10+3 
12  +  11 
5  +  10 

No.  14. 

11+6 
10+7 
6+3 
10+9 
12  +  10 

No.  1$. 

11+5 
12+9 
8  +  10 
9  +  11 
12  +  12 

EXERCISES  IN  SUBTRACTION. 


No.  10. 

13—4 
15  —  10 
16—6 
14  -12 
20  —  10 

No.  17. 

15  —  12 
13—7 
16—4 
18—9 
14—5 

No.  18. 

18—  3 
16—7 
13  —  12 
19—6 
21—3 

No.  19. 

21  —  10 
13  —  11 
15—  7 
22—7 
20  —  12 

No.  2O. 

14  —  11 
19—7 
16  —  12 
20—8 
21—6 

No.  21. 

15—  8 
13—6 

16  —  10 
23—7 

24—8 

No.  22. 

21—4 
19  —  10 
13—9 
15—  6 

20—7 

No.  23. 

19  —  12 
22  —  10 
24—6 
14—9 
23  —  11 

No.  24. 

20—6 
13—8 
16—9 
18  —  11 
17—  9 

No.  25. 

17  —  12 
24—7 
21—8 
15  —  11 

17—7 

No.  26. 

22—8 
19—9 
14—7 
,16—5 
23—9 

No.  27. 

22—4 
21—7 
14—8 
17  —  11 

18—6 

No.  28. 

21—9 
18  —  8 
23—6 
22—9 
19—8 

No.  29. 

24  —  10 
22—5 
16—8 
18—  7 
17—  8 

No.  3O. 

22  —  11 
17—  6 
24  —  12 

23—8 
21—5 

EXPLANATION  —  These  Tables  are  designed  for  a  brief  exercise  at 
the  beginning  or  close  of  the  daily  recitation,  and  should  be  dwelt 
upon  until  the  pupil  is  familiar  with  the  various  combinations.  Let 
the  pupil  recite  the  table  assigned  to  him,  as  the  signs  indicate ;  thus, 
in  No.  1,  4  and  3  are  7,  6  and  6  are  11,  ete. :  in  No.  16, 13  less  4  arc  9, 
etc.;  in  No.  81,  6  times  8  are  48,  etc.;  in  No.  46,  4  in  36,  9  times,  etc. 


REVIEW  TABLES. 


163 


EXERCISES  IN  MULTIPLICATION. 


No.  31. 

No.  33. 

No.  33. 

No.  34. 

No.  35. 

6X8 

4X5 

8X2 

5X7 

8X9 

5X4 

6X6 

9X4 

3X8 

5X5 

9X3 

3  X  12 

7X6 

6  X  12 

10  X     8 

7X2 

5X9 

10  X     3 

2  X  11 

6X4 

8X5 

7  X  11 

8X7 

7X8 

3X7 

No.  36. 

No.  37. 

No.  38. 

No.  39. 

No.  40. 

7X9 

9  X  12 

11  X  12 

5  X  10 

11  X     6 

4X8 

4X7 

12  X  11 

3X3 

9X2 

6X5 

3  X     1 

6X9 

12  X     5 

1  X     1 

8X8 

6  X  11 

4  X  10 

9X7 

12  X     3 

10  X    7 

5  X     8* 

9X8 

11  X     5 

6X7 

No.  41. 

No.  43. 

No.  43. 

No.  44. 

No.  45. 

12  X     9 

8  X  11 

12  X  12 

8X3 

11  X  11 

3  X  10 

4X9 

9X5 

12  X     7 

8X6 

8X4 

12  X     8 

7  X  12 

3  X  11 

9  X  11 

11  X    3 

10  X  H 

9X6 

7  X  10 

8  X  12 

4X4 

7X5 

11  X     9 

5  X  12 

12  X     6 

EXERCISES  IN  DIVISION. 


No.  46. 

36-5-4 
56-5-7 
42-5-6 
55-5-  11 

48-5-8 

No.  47. 

25-5-  5 
48-5-12 
45-5-9 
28-5-4 
100  -5-  10 

No.  48. 

72-5-9 
80-7-8 
27-5-9 
120-5-10 
99-5-11 

No.  49. 

36  H-  12 
49-5-7 
108-5-  9 
77-5-11 
18-5-3 

No.  5O. 

88  -5-  11 
84-5-12 
110-5-10 
99-5-9 
132  -5-  12 

No.  51. 

81-5-9 
18-7-6 
20-5-4 
35-5-5 

88-5-8 

No.  53. 

60-5-  10 
84-5-7 
33-5-11 
54-5-6 
60-f-  12 

,  No.  53. 

144  -5-  12 
63-5-9 
1  -5-  1 

32-5-8 
66  -5-  11 

No.  54. 

56-5-8 
35-5-7 
132-7-  11 
60-5-5 
110-5-11 

No.  55. 

121  -5-  11 
42-5-7 
96-7-12 
72-5-6 
54  -v-  9 

No.  56. 

64-5-8 
48-5-6 
120-5-  12 
44  -5-11 

70  -v-  7 

No.  57. 

33-5-3 
72-7-  12 
96-5-8 
66-5-6 
21-5-7 

No.  5S. 

45-5-5 

72-5-8 
63-7-7 
28-5-7 
108-5-  12 

No.  59. 

48-5-4 
36-5-9 
22-5-  11 
30-5-6 
27-5-3 

No.  60. 

36-5-6 
40-7-8 
32-5-4 
30-5-3 
90-7-9 

The  tables  may  be  profitably  used  in  many  ways.  The  columns  may 
be  added  upward  or  downward,  or  substituting  -f-  f°r  — >  X »  and  -5-, 
add  across  the  page.  Substituting  —  for  -5- ,  the  table  for  division 
becomes  a  table  for  subtraction.  By  dividing  the  dividend  of  one  ex- 
ample by  the  divisor  of  another,  mixed  numbers  maybe  obtained; 
thus,  in  Nos.  4G  and  47,  say  4  in  25,  5  in  36,  7  in  48,  etc. 


WRITTEN  ARITHMETIC. 


.1.  ON  page  26  the  pupil  has  learned  the  names  and 
meaning  of  the  ten  Arabic  figures,  0,  1,  2,  3,  4,  5,  6,  7,  8,  9; 
and  on  page  27  he  has  learned  the  names  and  uses  of  the 
signs,  $,  ~,  +,  — -,  X,  -T-- 

2.  The  learner  has  also  doubtless  observed  that  the 
value  of  a  figure  depends  not  only  on  the  figure  itself,  but 
also  on  the  place  the  figure  occupies  ;  for  example,  4, 
standing  alone,  means  four  units,  or  ones  ;  but  when  the  4 
is  made  to  occupy  the  second  place,  by  putting  0  or  any 
other  figure  on  the  right  of  it,  it  becomes  four  tens  ;''t\ms, 
40  equals  four  tens,  or  forty  ;  46  equals  four  tens  plus  six, 
that  is,  forty-six,  etc.  Again,  when  two  figures  are  at  the 
right  of  4,  the  4  becomes  four  hundreds,  which  equals  ten 
times  four  tens  ;  that  is,  each  remove  of  a  figure  one  place 
toward  the  left  makes  its  value  ten  times  as  much  as  it  was 
before.  This  will  be  seen  in  the  following  Table : 


C  °°        S3  °°  ** 

2  2  2, 2  2  2  =  Two  Wred  and  twenty-two  tnonsant  two  nnndrcd  and  twenty-two. 

327=  Three  hundred  and  twenty-se?en. 
5, 4  9  6  =  fire  thousand  four  hundred  and  ninefy-sii. 
6  0;  2  4  3  =  Sixty  thousand,  two  hundred  and  forty-three. 
6  0  1, 3  0  5  =  Sii  nundred  and  one  thousand,  three  hundred  and  fire. 


WRITTEN  ARITHMETIC.  1G5 

3.  Let  the  pupil  read  the  following  numbers  : 
1.  5G  5.  246  9.  3,742  13.     62,875 

•   2.  78  6.  307  10.  5,897  14.     80,94C 

3.  87  7.  843  11.  8,609  15.  384,600 

4.  95  8.  960  12.  9,054  16.  987,403 

4.    Write  the  following  numbers  in  figures  : 

1.  Forty-seven. 

2.  Sixty. 

3.  Two  hundred  and  seventy-nine. 

4.  Five  hundred  and  eight. 

5.  Three  thousand,  five  hundred  and  sixty-two. 

6.  Eight  thousand  and  two  hundred. 

7.  Sixty-two  thousand,  five  hundred  and  twenty. 

8.  One  hundred  and  six  thousand,  two  hundred  and  four. 

9.  Four  hundred  thousand,  four  hundred  and  thirteen. 

ADDITION. 

5.  BY  ADDITION  we  find  how  many  units  there  are  in 
two.  or  more  numbers  taken  together.     The  result  of  the 
addition  is  called  the  SUM,  or  AMOUNT. 

6.  To  add  when  the  amount  of  each  column  is  less  than 
ten. 

Ex.  1.  A  farmer  sold  125  bushels  of  corn,  342  bushels 
of  oats,  and  231  bushels  of  wheat  ;  how  many  bushels  of 
grain  did  he  sell  ?  Ans.  698. 

OPERATION. 

Having  set  the  numbers  so  that  units  stand 
342     under  units,  tens  under  tens,  etc.,  add  the  units  ; 
thus,  1  and  2  are  3,  and  5  are  8,  and  set  the  8 


Sum,  698     under  the  column  of  units.   Then  add  the  tens  ; 
thus,  3  and  4  are  7,  and  2  are  9,  and  set  the  9 
under  the  column  of  tens,  and  so  proceed  till  all  the  col- 
umns are  added. 

In  like  manner  add  the  following  examules  : 

2.  .  3.  4.  5.  6.  7.  8, 

143  311  126  2604  324  124  2143 

235  120  '211  4132  241  371  124 

421  247  242  1231  23  200  3010 


166  WBITTEN  ARITHMETIC. 

9.  10.         11.           12.         13.          14.  15. 

2101  1321       2144       2103       4162         203  2130 

2234  2134       3241         412       1304       5120  3247 

3120  3200       1302       3120       2013           62  1310 


16.  A  man  paid  $112  for  a  horse,  $235  for  a  chaise,  and 
$41  for  a  harness  ;  \vhat  did  he  pay  for  all  ? 

17.  A  gardener  has  231  apple  trees,  124  pear  trees,  322 
peach  trees,  and  200  cherry  trees ;  how  many  trees  has  he  ? 

18.  Add  together  205,  342,  120,  and  212. 

19.  Add  together  134,  213,  401,  and  141. 

20.  What  is  the  sum  of  1231,  8214,  and  4323  V 

21.  What  is  the  sum  of  5100,  1424,  and  2432  ? 

7.  To  add  when  the  amount  of  any  column  is  ten  or 
more. 

22.  A  man  bought  4  farms.     The  first  contained  345 
acres,  the  second  244  acres,  the  third  346  acres,  and  the 
fourth  638  acres ;  how  many  acres  were  there  in  the  4 
farms  ? 

OPERATION. 

345  We  find  the  sum  of  the  units  to  be  23,  or 
244     2  tens  and  3  units.     We  write  the  3  units 

346  under  the  column  of  units,  and  add  the  2  tens 
638     to  the  tens  in  the  next  column,  making  1 7  tens, 

Sum  1573  or  1  hundred  and  7  tens.  The  7  tens  are  writ- 
ten in  the  place  of  tens,  and  the  1  hundred, 
added  to  the  hundreds  in  the  example,  giving  15  hundreds, 
or  1  thousand  and  5  hundreds ;  and  when  these  figures  are 
written  in  their  respective  places,  the  example  is  solved. 

8.  In  the  same  manner  add  the  numbers  in  the  follow- 
ing short  columns  ;  also  add  across  the  page,  as  suggested  by 
the  signs. 

23.  4236*4-  3648  +  7264  +  8324  +  3663  +  2547 

24.  2743       2575       8923        7087       8729        3826 

25.  3254       1835       6845       3579       5273        9483 

26.  2572       1247       3468       9200       6004        6245 

27.  2356  -|-  1427  +  3240  -f  5124  +  6312  +  2436 

28.  5123       4172       3361        2534        1523       8240 

29.  3245       1843        C024       3201        5430       5376 

30.  2600       3412       5103        7120       6004       8241 


WRITTEN  ARITHMETIC.  167 

31.  4235  +  1063  -f  2714  +  3026  +  8124  +  3654 

32.  6004       2130         184  24         381         298 

33.  2146         401       8002         315  84       5423 

34.  2401        7103         516          284          511  27 

35.  1020  24  33       4123          871        4820 

36.  36427   -f  45326  -f-  52674  +  38956  -f  2138 

37.  54163  3402  254          4672         4694 

38.  72412         68240  3529  388         5368 

39.  43675  367         87006  54         2846 

40.  12341  3412  61          4102         3714 

41.  A  grain-dealer  bought  375  bushels  of  wheat  of  A, 
564  bushels  of  B,  2346  bushels  of  C,and  897  bushels  of  D  ; 
how  many  bushels  of  wheat  did  he  buy  ? 

42.  I  paid  $3464  for  a  farm,  $4875  for  a  house,  Si 5625 
for  a  mill,  and  $3875  for  30  shares  of  the  Boston  and  Maine 
Railroad  stock  ;  how  much  did  I  pay  for  all  this  property  ? 

43.  How  many  are  63  +  79  +  144  +  28  ?      Am.  314. 

44.  How  many  are  469  +  8742  +  92748  +  869  ? 

SUBTRACTION. 

9,  BY  SUBTRACTION  we  take  a  less  number  from  a 
greater  number  to  find  their  difference. 

The  greater  number  is  called  the  MINUEND;  the  less 
number,  the  SUBTRAHEND  ;  the  difference,  the  REMAIN- 
DER. 

10.  To  subtract  when  no  figure  in  tho  subtrahend  is 
larger  than  the  figure  over  it. 

Ex.  1.  From  748  take  236. 

OPERATION. 

Minuend,  ,   If.        Taking  6  from  8  leaves  2,  3  from  4 
Subtrahend,_236    leaveg  ^  ?  from  ?  Iea' 

Remainder,  512    fore,  the  remainder  is  512. 

2.  3.  4.  5. 

From   7658  5703  8287  68295 

Take   3427  4301  3144  36241 

Ans.     4231 

7.        8.       9.      10.       11. 
From  87426     70827     3547     7G13     35784 
Take  45105     40326     2136     2431     13251 


1G8  WRITTEN  ARITHMETIC. 

12.  A  farmer  bought  a  farm  for  $3625,  and  sold  it  for 
$4986  ;  how  much  did  he  gain  ?  Ans.  $1361. 

13.  In  1860  the  population  of  Maine  was  628276,  and 
that  of  New  Hamsphire  was  326072  ;  how  many  more  peo- 
ple were  there  in  Maine  than  in  New  Hampshire  ? 

11.  To  subtract  when  any  figure  in  the  subtrahend  is 
greater  than  the  figure  over  it. 

14.  From  982  take  137. 

OPERATION.  As  we  cannot  take  7  units  from  2  units, 
Mm.  982  one  Of  the  iens  jg  put  wjth  the  two  units,  mak- 
Sub.  137  jn«j  12  units;  and  then  7  units  from  12  units 
Hem.  845  leave  5  units.  Now  as  one  of  the  8  tens  has 
been  put  with  the  2  units,  only  7  tens  remain 
in  the  minuend,  and  3  tens  from  7  tens  leave  4  tens ;  and, 
finally,  1  hundred  from  9  hundreds  leaves  8  hundreds; 
therefore,  the  entire  remainder  is  845. 

12.  In  the  same  manner  solve  the  following  examples, 
taking  each  lower  number  from  the  one  over  it  in  each  ex- 
ample ;  also  subtract  in  the  manner  indicated  by  the  signs. 

„   <  6379  —  3245  8268  —  7614  8078  —  5384 

°'j  2184  — 1528  3427  —  2817  2635  —  1748 

(  7683  —  3846  9463  —  4879  5009  —  2743 

°- 1  5947  —  1072  8270  —  3948  2746  —  1834 

( 8725  —  3684  7000  —  4763  5948—3609 

'•J6943 —  2948  3749  —  3623  4782  —  2948 

(5402  —  3712  8760  —  2487  9046-8697 

J4802—    824  4837 —    948  5609 —    849 

(  6948  —  3879  5608  —  3742  5907  —  3764 

(4062  —  2983  4924—    936  3298  —  2643 

(  7829  —  6420  7869  —  3942  6308  —  5380 

u'}    943—    784  3842—    984  5709—    648 

C  8037  — 4682  9293  —  6354  8725  —  3648 

*••  |  5643  —  3486  8062—4630  4592  —  2000 

9  5  9999  —  6849  6849  —  5468  8234  —  6845 

"I  7864  —  5986  3784  —  2407  3729  —  2698 

23.  Washington  was  born  in  1732,  and  died  in  1799; 
at  what  age  did  he  die  ? 

24.  Methuselah  died  at  the  age  of  969   years,    and 
Washington  at  6  7 ;  what  was  the  difference  of  their  ages  ? 


WRITTEN  ARITHMETIC.  1G9 

25.  A  merchant  sold  goods  for  $3427,  and  thereby 
gained  $1224 ;  what  did  the  goods  cost  him  ? 

26.  In  a  certain   battle  27345   men  were  engaged  on 
one  side,  and  23598  on  the  other;  how  many  more  were 
engaged  on  one  side  than  on  the  other  ? 

27.  The  distance  round  the  earth  is  about  24856  miles, 
and  the  distance  through  it  is  about  7912  miles ;  how  much 
further  round  it  than  through  it  ? 

28.  How  many  years  have  passed  since  the  discovery 
of  America  in  1492  ? 

MULTIPLICATION. 

13.  BY  MULTIPLICATION  we  find  how  many  units 
there  are  in  any  number  of  times  a  given  number. 

The  number  to  be  repeated  is  called  the  MULTIPLI- 
CAND ;  the  number  which  shows  how  many  times  the  mul- 
tiplicand is  to  be  taken  is  called  the  MULTIPLIER  ;  the  re- 
sult of  the  multiplication  is  called  the  PRODUCT.  The 
Multiplicand  and  Multiplier  are  called  FACTORS. 

14.  To  multiply  by  a  single  figure. 

Ex.  1.  In  1  bushel  there  are  32  quarts ;  how  many 
quarts  are  there  in  9  bushels  ? 

OPERATION.          Having  set  the  factors  as  in  the  mar- 
Multiplicand,  32     gin,  we  say,  9  times  2  units  are  18  units 

Multiplier, 9     =  1  ten  and  8  units;  write  the  8  units 

Product  288  *n  units>  place,  and  tnen  Sa7»  9  times  3 
tens  are  27  tens,  which,  increased  by 
the  1  ten  previously  obtained,  make  28  tens  =  2  hundreds 
and  8  tens,  and  these,  written  in  the  place  of  hundreds 
and  tens  respectively,  give  the  true  product,  288qt. 


2. 

3. 

4. 

5. 

6. 

Multiplicand,   364 
Multiplier,            3 

573 
4 

7243 
5 

436 
6 

3405 
7 

Product,          1092 

2292 

36215 

2616 

23835 

7.                8. 

9. 

10. 

11. 

12. 

3259           2085 

3706 

8765 

7432 

5984 

6                 4 

2 

8 

5 

6 

170  WRITTEN  ARITHMETIC. 

13.  If  1  horse  is  worth  $125,  what  are  7  horses  worth  ? 

14.  In  1  year  there  are  365  days;  how  many  days  are 
there  in  3  years  ? 

15.  If  the  President  of  the  United  States  saves  $5648 
in  1  year,  how  much,  at  the  same  rate,  will  he  save  in  4 
years  ? 

16.  How  many  yards  of  cloth  are  therein  9  bales,  each 
bale  containing  625  yards  ? 

1 7.  Multiply  356  by  7.  21.  3742  X  8  =  ? 

18.  Multiply  874  by  3.  22.  6536  X  6  =  ? 

19.  Multiply  368  by  5.  23.  3042  X  2  =  ? 

20.  Multiply  759  by  4.  24.  7608  X  9  =  ? 

15.  To  multiply  by  two  or  more  figures. 

25.  How  many  quarts  are  there  in  49  bushels  ? 

u  OPERATION.  First  multiply  by  9,  as  though  9 
Multiplicand,  32  were  the  only  figure  in  the  multi- 
Multiplier,  49  plicr;  then  multiply  by  4,  and  set 

Partial             f    288  t^ie  ^rst  ^Sure  °f  tn^s  product  under 

Products         "1  1 28  tQe  4 ;  finally,  add  the  partial  prod- 

ucts  together,  and  the  sum  will  be 

True  product,   1568  the  true  product. 

16.  In  the  same  manner  solve  the  following  examples, 
multiplying  each  upper  number  by  the  one  under  it  in  each 
example ;  also  multiply  in  the  manner  indicated  by  the  signs* 

,   (  345  X  24  504  X  32  7063  X  25 

D<  |    37  X  56  56  X45  62  X  74 

97  ?  432X243  524X325  540X367 

*  I  724  X    36  464  X  426  842  X  304 

9«   (  4326  X  28  6304  X  56  3068  X  384 

5'|    325X32  542X72  247X265 

(  5648  X  59  4008  X  63  5308  X  872 

(    364  X  38  3604  X  75  204"6  X  635 

0  j  3564  X  48  9604  X  49  6350  X  358 

j  2435X84  376X84  4635X496 

5642  X  67  4768  X  95  3465  X  386 

325X84  347X46  7308X947 

.32.    If  a  steamboat  sails  288  miles  per  day,  how  far  will 
she  sail  in  27  days? 


WRITTEN  ARITHMETIC.  171 


DIVISION. 

17.  BY  DIVISION  we  find  how  many  times  one  number 
is  contained  in  another. 

The  number  to  be  divided,  is  called  the  DIVIDEND  ; 
the  number  by  which  to  divide  is  called  the  DIVISOR; 
the  number  of  times  the  dividend  contains  the  divisor  is 
called  the  QUOTIENT.  If  anything  is  left  after  dividing, 
it  is  called  the  REMAINDER. 

1§.     To  perform  Short  Division. 

Ex.  1.  How  many  weeks  are  there  in  364  days  ? 

OPERATION.  In  dividing  we  first  say,  7  in 

Divisor,  7)364  Dividend.     36,  5  times  and  1  remainder; 

Quotient      52  set  *ne  qu°tient»  5,  under  the  6 

of  the  dividend,  and  then,  im- 
agining the  remainder,  1,  placed  before  the  4,  say,  7  in  14, 
2  times ;  set  the  2  under  the  4,  and  thus  we  find  the  quo- 
tient, 52.  This  process  is  called  Short  Division. 

2.  3.  4.  5. 

Divisor,  6)102  Dividend.          5)875          8)432          6)456 

Quotient,     27 

6.  7.  8.  9.  10. 

7)4417  8)4504  2)1764  3)2847  5)3465 

11.  12.  13.  14.  15. 

4)2296  9)2916  7)3122  8)4320  6)3?16 

16.  How  much  sugar,  at  9  cents  a  pound,  can  be  bought 
for  342  cents,  or  $3.42  ?  Ans.  38lb. 

1 7.  How  many  pigs,  at  $5  each,  can  be  bought  for  $285  ? 

18.  If  a  horse  travels  7  miles  per  hour,  in  how  many 
hours  will  he  travel  1001  miles  ? 

19.  Divide  161  by  7.  24.  9732— -4  =  ? 

20.  Divide  204  by  6.  25.  1768  —  2  —  ? 

21.  Divide  475  by  5.  26.  7648  —  8  —  ? 

22.  Divide  345  by  3.  27.4428  —  6  —  ?       ' 

23.  Divide  846  by  9.  28.  3762  —  9:=:? 


172 


WRITTEN  ARITHMETIC. 


45_ 
43 

£i 

72 
72 


19.  To  perform  Long  Division. 

Ex.  29.  Paid  $4932  for  9  acres  of  land  \  what  was  the 
price  per  acre  ? 

Having  set  the  divisor  and  dividend  as  in 
Short  Division,  draw  a  curve  at  the  right  of  the 
dividend,  and  then  say,  9  in  49,  5  times,  and  set 
the  5  at  the  right  of  the  dividend.      Then 
multiply  the  divisior  by  the  quotient,  5,  and  set 
the  product,  45,  under  the  49  of  the  dividend, 
and  substract  the  45  from  the  49.     To  the  re- 
mainder, 4,  annex  3,  the  next  figure  of  the 
0          dividend,  so  forming  a  new  partial  dividend, 
and  then  say,  9  in  43, 4  times,  and  set  the  4  as 
the  next  figure  of  the  quotient.     Multiply  the  divisor  by 
this  new  quotient-figure,  and  substract  the  product  from  the 

Sartial  dividend.     Proceed  in  this  manner  until  the  whole 
ividend  has  been  divided.     This  is  called  Long  Division. 

2O.  In  the  same  manner  solve  the  following  examples  ; 
also  divide  in  the  manner  indicated  by  the  signs. 

32. 
13)4753(365 

85 

~73 

_65 

Remainder,  8 

90090—195 
4095—  15 
S51900-7-391 
9775—  23 

12463  —  816 
3746—  24 


30. 
8)3568(446 

— 
36 

— 
48 
48 


31. 

12)6564(547 
60 

~66 
48 

84 
84 


33. 


Divide      1728—    72 
By  144—    12 


o,    (  Divide  309 120—  805 

(By  25760—    23 

Q-   (Divide    46385  —  563 

5'{By  2435—   42 

0«   (Divide    54687  —  348 

Sb'JBy  2731—   16 


27462- 


3724—    39 


948 


87.  How  much  tea,  at  35  cents  per  pound,  can  be  bought 
for  $8. 75? 


WRITTEN  ARITHMETIC  173 

38.  How  much  flour,  at  $9  per  barrel,  can  be  bought  for 
$3762? 

3D.  In  how  many  days  can  a  man  walk  252  miles,  if  he 
walks  21  miles  per  day  ? 

40.  How  many  days  are  there  in  1 728  hours  ? 

41.  How  many  dollars  in  3168  shillings,  if  6  shillings  make 
a  dollar  ?    If  8  shillings  make  a  dollar  ? 

42.  In  how  many  days  will  a  ship  sail  5040  miles,  if  ghe 
sails  144  miles  per  day  ? 

43.  A  drover  paid  $1431  for  27  oxen ;  what  was  the  av- 
erage price  per  ox  ? 

44.  In  how  many  hours  will  a  locomotive  run  1225  miles, 
if  it  runs  25  miles  per  hour  ? 

45.  A  farmer  raised  1458  bushels  of  corn  on  27  acres; 
how  many  bushels  per  acre  did  he  raise  ? 

REDUCTION. 

21.  From  the  Lessons  in  Section  V,  the  learner  will 
readily  see  the  nature  of  the  following  examples.  The 
changing  or  reducing  numbers  from  one  name  or  denomi- 
nation to  another,  without  altering  their  values,  is  called 
REDUCTION. 

1.  In  3bush.  2pk.  5qt.  Ipt.  how  many  pints  ? 

OPERATION. 

bigh.pk.qt.pt.  Mult|ply   t]ie    3    by4    to    change    the 

4  bushels  to  pecks ;  to  the  product,  12,  add 

the  2pk.  given  in  the  example,  and  the 

14  pk.  result  is  14pk. ;  then  multiply  the  14  by  8 

8  to  cnanSe  tnc  pecks  to  quarts ;  to  the  pro- 

117qt  duct,  112,  add  the  5qt.  in  the  example, 

2  and  the  result  is  1 1 7qt. ;  so  proceed  till 

— -  the  example  is  solved. 
235  pt,  Ans. 

2.  In  5gal.  3qt.  Ipt.  2gi.  how  many  gills  ? 

3.  In  3£  4s.  9d.  Sqr.  how  many  farthings  ? 

4.  In  3wk.  4d.  6h.  12m.  20sec.  how  many  seconds? 

5.  In  4yd.  2ft.  7in.  how  many  inches  ? 

6.  Reduce  7yd.  3qr.  2na.  to  nails. 

7.  Reduce  3sq.m.  320a.  2r.  20sq.  rd.  to  rods. 

8.  Reduce  3c.  5c.ft.  12cu.ft.  1654c.in.  to  inches. 


174  WRITTEN  ARITHMETIC. 

9.  Change  1843qr.  to  pounds,  shillings,  etc. 
OPERATION.  First  divide  by  4  to  reduce  the  far- 

t)1843qr.  things  to  pence,  giving  460d.  and  3qr. ; 

12)460d.  +  3qr.    then  divide  the  460  by  12  to  reduce  pence 
to  shillings,  giving  38s.  and  4d. ;  then  di- 
4a<     vide  the  38  by  20  to  reduce  shillings  to 
l£  -f-  18s.   pounds,  and  thus  obtain  the  Ans. 
ylns.l£l8s.4d.8qr. 

10.  Change  387na.  to  yards,  quarters,  etc. 

11.  Change  l6879gr.Troy  Weight  to  pounds,  ounces,  etc 

12.  Change  1 68  79gr.  Apothecaries'  Weight  to  pounds,  etc, 

13.  Change  71G893dr.  to  tons,  etc. 

14.  Reduce  5327rd.  to  miles,  furlongs,  etc. 

15.  Reduce  47386sq.  in.  to  square  yards,  etc. 

16.  Reduce  356482c.  in.  to  cubic  yards,  etc. 

1 7.  Reduce  876gi.  to  gallons,  quarts,  etc. 

18.  Reduce  647pt.  to  bushels,  pecks,  etc. 

19.  Reduce  753986sec.  to  weeks,  days,  etc. 

20.  At  5c.  a  gill,  what  will  3gal.  2qt.  Ipt.  3gi.of  wine  cost  ? 

21.  At  3c.  apiece,  what  will  3  gross,  5  dozen,  and  6  but- 
tons cost  ? 

22.  At  2c.  a  sheet,  what  will  3  reams,  6  quires,  and  8 
sheets  of  paper  cost? 

23.  At  $1G  per  ounce,  what  are  3  Ib.  7oz.  of  gold  worth  ? 

24.  At  2c.  per  ounce,  what  are  15  Ib.  14oz.  of  iron  worth  ? 

25.  At  2c.  a  pint,  what  are  Sbush.  3pk.  6qt.  Ipt.  of  corn 
worth  ? 

26.  If  loz.  of  iron  will  make  3  nails,  how  many  nails  may 
be  made  of  7  Ib.  15oz.  of  iron  ? 

27.  At  2c.  a  pint,  what  are  5gal.  2qt.  Ipt.  of  milk  worth  ? 

28.  At  3c.  apiece,  what  are  6  dozen  and  9  oranges  worth  ? 

29.  At  2c.  apiece,  what  are  3  score  and  15  lemons  worth  ? 

MISCELLANEOUS  EXAMPLES. 

1.  Mr.  Stone  had  364  acres  of  land  in  one  piece,  and 
274  acres  in  another  piece  ;  but  he  has  sold  125  acres  from 
the  first,  and  94  acres  from  the  other ;  how  many  acres  has 
he  now  ? 

2.  Mr.  Pray  paid  $115  for  one  piece  of  carpet,  and 
$112  for  another;  he  sold  both  pieces  for  $250  ;  how  much 
did  he  gain  V 


WRITTEN  ARITHMETIC.  175 

3.  What  is  the  value  of  65  acres  of  land  at  $137  per 
acre? 

4.  How  many  men  are  there  in  a  regiment  of  15  com- 
panies, having  133  men  in  each  company  ? 

5.  What  will  36  barrels  of  flour  cost,  if  9  barrels  cost 
$99? 

6.  What  will  13  acres  of  land  cost,  if  52  acres  cost 
$7488? 

7.  If  12  men  can  cut  60  cords  of  wood  in  a  week,  how 
many  cords  can  1 7  men  cut  in  the  same  time  ? 

8.  How  many  rods  are  there  in  875  miles,  5  furlongs, 
and  33  rods? 

9.  How  many  farthings  are  there  in  354£  17s.  9d.  Iqr.  ? 

10.  A  man  has  two  farms  which  together  contain  432 
acres,  and  one  farm  is  7  times  as  large  as  the  other ;  how 
many  acres  are  there  in  each  ? 

11.  Divide  1728  into  two  such  parts  that  the  first  shall 
be  11  times  as  large  as  the  second. 

12.  Reduce  940819  drams  to  tons,  etc. 

13.  Reduce  907336  seconds  to  weeks,  days,  etc. 

14.  If  a  man*  can  walk  23  miles  per  day,  in  how  many 
days  can  he  walk  391  miles? 

15.  A  road-builder  employed  33  men,  giving  the  same 
wages  to  each,  and  at  the  end  of  2  months  it  took  $1584  to 
pay  them  ;  what  were  the  wages  of  each  per  month  ? 

16.  In  a  certain  house  there  are  8  rooms,  having  3  win- 
dows in  each  room,  and  12  panes  of  glass  in  each  window  ; 
how  many  panes  of  glass  are  there  in  the  house  ? 

1 7.  A  merchant  having  3  pieces  of  cloth  measuring  63yd., 
45yd.,  and  56yd.  severally,  sold  22yd.  from  the  first,  31yd. 
from  the  second,  and  14yd.  from  the  third ;  how  many 
yards  had  he  remaining? 

18.  Mr.  Holt  owed  $3462,  but  paid  $1362  in  May,  and 
$897  in  June  ;  how  much  did  he  still  owe? 

19.  How  many  are  876  -f  392  -f  648  —  987  ? 

20.  How  many  are  689 -f- 9642  +  87  —  398? 

21.  From  the  sum  of  384  and  426,  take  the  difference 
between  567  and  432. 

22.  How  many  are  876  X  43  ?   968  X  382  ? 

23.  How  many  are  1584 -r- 66?    21364-^763? 

24.  How  many  are  38X46  —  24  X  26  ? 

25.  How  many  are  87  X  33  +  36  X  27  ? 

26.  What  cost  54  tons  of  hay,  at  $18  per  ton  ? 


17G  WRITTEN  ARITHMETIC. 

27.  A  farmer  sold  75  bushels  of  wheat,  at  $2  per  bushel, 
for  which  he  received  15  yards  of  cloth,  at  $4  per  yard,  and 
the  balance  in  money ;  how  much  money  did  he  receive? 

28.  A  man's  income  is  $1687  a  year,  and  his  expenses 
ani  Si  a  day ;  what  does  he  save  in  a  year  of  365  days ? 

29.  The  earth,  in  going  round  the  sun,  moves  19  miles 
per  second ;  how  far  does  it  move  in  an  hour  ? 

30.  Light  moves  192000  miles  in  a  second;  how  far  does 
it  move  in  an  hour  ? 

31.  I  owe  3  notes,  whose  sum  is  $368.      One  of  these 
notes  is  for  $  1 25,  another  for  $84 ;  for  what  is  the  third  one  ? 

32.  A  and  B  start  from  the  same  place,  and  travel  in  the 
Fmne  direction,  A  at  the  rate  of  48  miles,  and  B  G4  miles 
per  day ;  how  far  apart  are  they  in  1  day  ?    In  24  days  ? 

33.  A  and  B  start  from  the  same  place,  and  travel  in  op- 
posite directions,  A  at  the  rate  of  36  miles,  and  B  44  miles, 
per  day  ;  how  far  apart  are  they  in  35  days  ? 

34.  The  President  of  the  United  States  receives  a  salary 
of  $25000  a  year;  what  will  he  save  in  a  year  of  365  days, 
if  his  expenses  are  &40  per  day  ? 

35.  In  1  hogshead  of  wine  there  are  (?3  gallons  ;  how 
many  gallons  in  36  hogsheads  ? 

36.  How  many  yards  of  cloth  in  25  bales,  each  bale  con- 
taining 54  pieces,  and  each  piece  36  yards  ? 

37.  The  last  transit  of  Venus  across  the  sun's  face  was 
in  1769,  and  the  next  will  be  in  1874  ;  how  many  years 
between  these  two  transits  ? 

38.  Bonaparte  was  born  in  the  year  1769,  and  lived  52. 
years ;  in  what  year  did  he  die  ? 

39.  The  first  settlement  in  New  England  was  made  at 
Plymouth  in  1620 ;  how  many  years  is  it  since  that  time  ? 

40.  How  long  since  the  Declaration  of  American  Inde^ 
pendence  in  1776  ? 

41.  A  rectangular  piece  of  ground-  is  72  rods  long  and 
36  rods  wide  ;  how  many  square  rods  are  there  in  the  piece  ? 
How  many  rods  is  it  round  the  piece  ? 

42.  Apiece  of  ground  is  42  rods  square;  what  will  it 
cost  to  build  a  wall  around  it,  at  &2:per  rod  ?     What  is  the 
piece  of  ground  worth,  at  $3  per  square  rod? 


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UNIVERSITY  OF  CALIFORNIA  LIBRARY 


STANDARD  ARITHMETICS. 

EATOiVS    COMPLETE    SERIES, 

ADAPTED  TO  THE  BEST  MODE  OF  INSTltt'CTIOX. 


TIIK     1-T1.I 

I.  Eaton's  I»rimai.'y    Aril  lime  tie. 

II.  IEa  toil's  Intellectual    Aritlnuotio. 

III.  JSatoiiV*  C'ormiio   *      Hioliool     A.r  ilium  e  tie 

IV.  Eaton's  IVew   rJLVo:il  Lsc;    on-   A-i'ltlxinotio 

Till  ISUKD    BY 

1.  TIic  thorough  and   scientific  manner  in  which  all  the  principles  ar 

developed  and  illustrated. 

2.  T'  -aid  brevity  of  its  rules  and  definitions. 

3.  The  logical  and  satisfactory  explanations. 

4.  The  prominence  of*  ANALYSIS  throughout  the  scries. 

5.  The  practical  character  of  each  ' 

G.     The  lieiny  based  upon  the  inductive  and  analytical  plan,  which  tcnclu 

ihe  i)iipil  to  thi.ilc  au«i 
7.    The  mechanical  style  in  wlre'i  tho  books  are  manufactured. 

THE  PEIMAEY"~AEITEMETIO 

Follows  the  same  general  plan,  Improved    w'jich  has  made  COLBURX' 

i   in  mental  arithmetic,  for  the  las 

quarter  of  a  •!  essentially  to  be  a  Primary  Jiooi 

and  to  render  the    subject    of    numbers    ATTRACTIVE    and    K.\SY    ft 

THE    INTELLECTUAL    AEITHMETIO, 

This  is  a  new  Mental  Arithmetic,  for  advanced  classes,  on  the  a^ov 
plan.    While  it  will  retain  tin-  «  x  «.•«•!  'nioes  of  the  system  of  "\VAKHK 
RN,  it  will  contain  tlie  iiapro\  oments  in  teaching  developed  sine 
Jus  time. 

THE  COMMON  SCHOOL  AEITHMETIC 

Js  a  complete  text-book  on  the  subject  of  Written  Arithmetic,  designe 
for  use  in  all  COMMON  ?id  GRAMMAR  SCHOOLS. 

THE  NEW  TEEATISE  ON  WRITTEN  AEITHMETIO 

Is  the  most  thorough  and  scientific  troal'-:  on  this  subject  which  has  ev< 
appeared.    The  accurate  style  of  rea>omii£,  ir.d  the  philosophical  arrang- 
ud  development  of  topi«  a  for  this  book  a  large  circul 

tion.    It  is  desi^u^d  foi  Grammar  and  High  Schools,  and  Academies. 

These  books  have  the  unqualified  recommendation  of  the  most  prom 
neut  educators. 


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